Le, Maohua; Styer, Robert On a conjecture concerning the number of solutions to \(a^x+b^y=c^z\). (English) Zbl 07734852 Bull. Aust. Math. Soc. 108, No. 1, 40-49 (2023). MSC: 11D61 11D45 PDF BibTeX XML Cite \textit{M. Le} and \textit{R. Styer}, Bull. Aust. Math. Soc. 108, No. 1, 40--49 (2023; Zbl 07734852) Full Text: DOI
Dujella, Andrej; Győry, Kálmán; Michaud-Jacobs, Philippe; Pintér, Ákos On power values of pyramidal numbers. II. (English) Zbl 07732767 Acta Arith. 208, No. 3, 199-213 (2023). MSC: 11D41 11D59 11D61 14G99 PDF BibTeX XML Cite \textit{A. Dujella} et al., Acta Arith. 208, No. 3, 199--213 (2023; Zbl 07732767) Full Text: DOI arXiv
Heintze, Sebastian; Tichy, Robert F.; Vukusic, Ingrid; Ziegler, Volker On the Diophantine equation \(U_n - b^m = c\). (English) Zbl 07729929 Math. Comput. 92, No. 344, 2825-2859 (2023). MSC: 11Y50 11D61 11B37 11J86 PDF BibTeX XML Cite \textit{S. Heintze} et al., Math. Comput. 92, No. 344, 2825--2859 (2023; Zbl 07729929) Full Text: DOI arXiv
Tadee, Suton; Thaneepoon, Nuanchuen On the Diophantine equation \(6^x+p^y=z^2\), where \(p\) is prime. (English) Zbl 07716255 Int. J. Math. Comput. Sci. 18, No. 4, 737-741 (2023). MSC: 11D61 PDF BibTeX XML Cite \textit{S. Tadee} and \textit{N. Thaneepoon}, Int. J. Math. Comput. Sci. 18, No. 4, 737--741 (2023; Zbl 07716255) Full Text: Link
Luca, Florian; Zottor, Faith S. On \(Y\)-coordinates of Pell equations which are Fibonacci numbers. (English) Zbl 07716029 Bol. Soc. Mat. Mex., III. Ser. 29, No. 2, Paper No. 49, 43 p. (2023). MSC: 11D61 11B39 11D45 PDF BibTeX XML Cite \textit{F. Luca} and \textit{F. S. Zottor}, Bol. Soc. Mat. Mex., III. Ser. 29, No. 2, Paper No. 49, 43 p. (2023; Zbl 07716029) Full Text: DOI
Mina, Renz Jimwel S.; Bacani, Jerico B. On the Diophantine equation \(p^x + (p+5)^y = Z^2\), where \(p\) is odd prime. (English) Zbl 07714843 Thai J. Math. 21, No. 1, 67-75 (2023). MSC: 11D72 11D61 14H52 11A15 PDF BibTeX XML Cite \textit{R. J. S. Mina} and \textit{J. B. Bacani}, Thai J. Math. 21, No. 1, 67--75 (2023; Zbl 07714843) Full Text: Link
Kitayama, Hidetaka; Tagawa, Hiroyuki; Urahashi, Keiichi Jeśmanowicz’ conjecture for non-primitive Pythagorean triples. (English) Zbl 07692662 Period. Math. Hung. 86, No. 2, 442-453 (2023). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11D61 PDF BibTeX XML Cite \textit{H. Kitayama} et al., Period. Math. Hung. 86, No. 2, 442--453 (2023; Zbl 07692662) Full Text: DOI
Luca, Florian; Noubissie, Armand Linear combinations of factorial and \(S\)-unit in a ternary recurrence sequence with a double root. (English) Zbl 07692661 Period. Math. Hung. 86, No. 2, 422-441 (2023). Reviewer: Ranjeet Sehmi (Chandigarh) MSC: 11B65 11D61 PDF BibTeX XML Cite \textit{F. Luca} and \textit{A. Noubissie}, Period. Math. Hung. 86, No. 2, 422--441 (2023; Zbl 07692661) Full Text: DOI
Viriyapong, Chokchai; Viriyapong, Nongluk On the Diophantine equation \(a^x+(a+2)^y=z^2\), where \(a\equiv_{21}5\). (English) Zbl 07689943 Int. J. Math. Comput. Sci. 18, No. 3, 525-527 (2023). MSC: 11D61 PDF BibTeX XML Cite \textit{C. Viriyapong} and \textit{N. Viriyapong}, Int. J. Math. Comput. Sci. 18, No. 3, 525--527 (2023; Zbl 07689943) Full Text: Link
Viriyapong, Nongluk; Viriyapong, Chokchai On the Diophantine equation \(255^x+323^y=z^2\). (English) Zbl 07689942 Int. J. Math. Comput. Sci. 18, No. 3, 521-523 (2023). MSC: 11D61 PDF BibTeX XML Cite \textit{N. Viriyapong} and \textit{C. Viriyapong}, Int. J. Math. Comput. Sci. 18, No. 3, 521--523 (2023; Zbl 07689942) Full Text: Link
Gayo, William S. jun.; Bacani, Jerico B. On the solutions of some Mersenne prime-involved Diophantine equations. (English) Zbl 07689939 Int. J. Math. Comput. Sci. 18, No. 3, 487-495 (2023). MSC: 11A41 11D61 11D72 PDF BibTeX XML Cite \textit{W. S. Gayo jun.} and \textit{J. B. Bacani}, Int. J. Math. Comput. Sci. 18, No. 3, 487--495 (2023; Zbl 07689939) Full Text: Link
Pintoptang, Umarin; Tadee, Suton The complete set of non-negative integer solutions for the Diophantine equation \((pq)^{2x}+p^y=z^2\), where \(p,q,x,y,z\) are non-negative integers with \(p\) prime and \(p\nmid q\). (English) Zbl 07663624 Int. J. Math. Comput. Sci. 18, No. 2, 205-209 (2023). MSC: 11D61 PDF BibTeX XML Cite \textit{U. Pintoptang} and \textit{S. Tadee}, Int. J. Math. Comput. Sci. 18, No. 2, 205--209 (2023; Zbl 07663624) Full Text: Link
Tadee, Suton; Poopra, Sudaporn On the Diophantine equation \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{n}\). (English) Zbl 07663621 Int. J. Math. Comput. Sci. 18, No. 2, 173-177 (2023). MSC: 11D61 PDF BibTeX XML Cite \textit{S. Tadee} and \textit{S. Poopra}, Int. J. Math. Comput. Sci. 18, No. 2, 173--177 (2023; Zbl 07663621) Full Text: Link
Tadee, Suton; Laomalaw, Napalai On the Diophantine equation \((p+2)^x-p^y=z^2\), where \(p\) is prime and \(p\equiv5\pmod{24}\). (English) Zbl 07663618 Int. J. Math. Comput. Sci. 18, No. 2, 149-152 (2023). MSC: 11D61 PDF BibTeX XML Cite \textit{S. Tadee} and \textit{N. Laomalaw}, Int. J. Math. Comput. Sci. 18, No. 2, 149--152 (2023; Zbl 07663618) Full Text: Link
Orosram, Wachirarak; Tangjai, Wipawee On the Diophantine equation \((pq)^x+(pq)^{2s}n^y=z^2\), where \(p\) and \(q\) are prime numbers. (English) Zbl 07663617 Int. J. Math. Comput. Sci. 18, No. 2, 143-147 (2023). MSC: 11D61 PDF BibTeX XML Cite \textit{W. Orosram} and \textit{W. Tangjai}, Int. J. Math. Comput. Sci. 18, No. 2, 143--147 (2023; Zbl 07663617) Full Text: Link
Fujita, Yasutsugu; Le, Maohua; Terai, Nobuhiro A note on the number of solutions of ternary purely exponential Diophantine equations. (English) Zbl 1510.11094 Bull. Aust. Math. Soc. 107, No. 1, 53-65 (2023). Reviewer: Ilker Inam (Bilecik) MSC: 11D61 PDF BibTeX XML Cite \textit{Y. Fujita} et al., Bull. Aust. Math. Soc. 107, No. 1, 53--65 (2023; Zbl 1510.11094) Full Text: DOI
Dimitrov, Stoyan A diophantine equation involving special prime numbers. (English) Zbl 07655760 Czech. Math. J. 73, No. 1, 151-176 (2023). MSC: 11L07 11L20 11P32 PDF BibTeX XML Cite \textit{S. Dimitrov}, Czech. Math. J. 73, No. 1, 151--176 (2023; Zbl 07655760) Full Text: DOI
Srimud, Kulprapa; Tadee, Suton On the diophantine equation \(3^x+b^y=z^2\). (English) Zbl 1513.11112 Int. J. Math. Comput. Sci. 18, No. 1, 137-142 (2023). MSC: 11D61 PDF BibTeX XML Cite \textit{K. Srimud} and \textit{S. Tadee}, Int. J. Math. Comput. Sci. 18, No. 1, 137--142 (2023; Zbl 1513.11112) Full Text: Link
Siraworakun, Apirat; Tadee, Suton Solutions of the Diophantine equation \(p^x+q^y=z^2\), where \(p,q\equiv 3\pmod 4\). (English) Zbl 1513.11111 Int. J. Math. Comput. Sci. 18, No. 1, 131-136 (2023). MSC: 11D61 PDF BibTeX XML Cite \textit{A. Siraworakun} and \textit{S. Tadee}, Int. J. Math. Comput. Sci. 18, No. 1, 131--136 (2023; Zbl 1513.11111) Full Text: Link
Gómez, Carlos A.; Gómez, Jhonny C.; Luca, Florian On a variant of an identity relating cubes of three consecutive Fibonacci numbers. (English) Zbl 1516.11023 Bull. Malays. Math. Sci. Soc. (2) 46, No. 2, Paper No. 47, 31 p. (2023). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11B39 11D61 11J86 PDF BibTeX XML Cite \textit{C. A. Gómez} et al., Bull. Malays. Math. Sci. Soc. (2) 46, No. 2, Paper No. 47, 31 p. (2023; Zbl 1516.11023) Full Text: DOI
Bennett, Michael A.; Siksek, Samir Differences between perfect powers: the Lebesgue-Nagell equation. (English) Zbl 07618833 Trans. Am. Math. Soc. 376, No. 1, 335-370 (2023). MSC: 11D61 11D41 11F80 11F03 PDF BibTeX XML Cite \textit{M. A. Bennett} and \textit{S. Siksek}, Trans. Am. Math. Soc. 376, No. 1, 335--370 (2023; Zbl 07618833) Full Text: DOI arXiv
Hamtat, Abdelkader On the Diophantine equation on reciprocal Fibonacci numbers. (English) Zbl 07716313 Math. Appl. (Warsaw) 50, No. 2, 249-254 (2022). MSC: 11D61 11B39 PDF BibTeX XML Cite \textit{A. Hamtat}, Math. Appl. (Warsaw) 50, No. 2, 249--254 (2022; Zbl 07716313) Full Text: DOI
Luca, Florian Markov triples with two Fibonacci components. (English) Zbl 07673828 Rend. Semin. Mat. Univ. Padova 148, 213-243 (2022). MSC: 11B39 11D61 PDF BibTeX XML Cite \textit{F. Luca}, Rend. Semin. Mat. Univ. Padova 148, 213--243 (2022; Zbl 07673828) Full Text: DOI
Alahmadi, Adel; Luca, Florian On a result of Fujita and Le. (English) Zbl 07672120 Acta Sci. Math. 88, No. 3-4, 577-580 (2022). MSC: 11D41 11N37 PDF BibTeX XML Cite \textit{A. Alahmadi} and \textit{F. Luca}, Acta Sci. Math. 88, No. 3--4, 577--580 (2022; Zbl 07672120) Full Text: DOI
Hoque, Azizul Generalized Mersenne numbers of the form \(cx^2\). (English) Zbl 07670586 Ann. Math. Inform. 55, 88-92 (2022). MSC: 11D61 11N32 PDF BibTeX XML Cite \textit{A. Hoque}, Ann. Math. Inform. 55, 88--92 (2022; Zbl 07670586) Full Text: DOI arXiv
Alan, Murat Mersenne numbers as a difference of two Lucas numbers. (English) Zbl 07655799 Commentat. Math. Univ. Carol. 63, No. 3, 269-276 (2022). MSC: 11B39 11J86 11D61 PDF BibTeX XML Cite \textit{M. Alan}, Commentat. Math. Univ. Carol. 63, No. 3, 269--276 (2022; Zbl 07655799) Full Text: DOI
Luo, Raymond; Yu, Gang A ternary additive problem involving fractional powers. (English) Zbl 07651338 Involve 15, No. 4, 629-640 (2022). MSC: 11D85 11L07 PDF BibTeX XML Cite \textit{R. Luo} and \textit{G. Yu}, Involve 15, No. 4, 629--640 (2022; Zbl 07651338) Full Text: DOI
Meher, N. K.; Rout, S. S. \(S\)-parts of sums of terms of linear recurrence sequences. (English) Zbl 07650960 Acta Math. Hung. 168, No. 2, 553-571 (2022). Reviewer: István Pink (Debrecen) MSC: 11B37 11D61 11J86 PDF BibTeX XML Cite \textit{N. K. Meher} and \textit{S. S. Rout}, Acta Math. Hung. 168, No. 2, 553--571 (2022; Zbl 07650960) Full Text: DOI arXiv
Edjeou, Bilizimbéyé; Faye, Bernadette; Gómez, Carlos A.; Luca, Florian On \(Y\)-coordinates of Pell equations which are Lucas numbers. (English) Zbl 1506.11043 Ramanujan J. 59, No. 4, 1091-1136 (2022). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D61 11B39 11D45 PDF BibTeX XML Cite \textit{B. Edjeou} et al., Ramanujan J. 59, No. 4, 1091--1136 (2022; Zbl 1506.11043) Full Text: DOI
Abu Muriefah, Fadwa S.; Le, Maohua; Soydan, Gökhan A note on the Diophantine equation \(x^2 =4p^n -4p^m +\ell^2\). (English) Zbl 1505.11057 Indian J. Pure Appl. Math. 53, No. 4, 915-922 (2022). Reviewer: Maciej Ulas (Kraków) MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{F. S. Abu Muriefah} et al., Indian J. Pure Appl. Math. 53, No. 4, 915--922 (2022; Zbl 1505.11057) Full Text: DOI
Dima, Andreea A computer-based approach to solving the Diophantine equation \(7^x-3^y=100\). (English) Zbl 07613145 PUMP J. Undergrad. Res. 5, 161-164 (2022). MSC: 11D61 11Y50 PDF BibTeX XML Cite \textit{A. Dima}, PUMP J. Undergrad. Res. 5, 161--164 (2022; Zbl 07613145) Full Text: Link
Terai, Nobuhiro; Nakashiki, Saya; Suenaga, Yudai On the generalized Ramanujan-Nagell equation \(x^2 + b^m = c^n\) with \(a^2 + b^r = c^2\). (English) Zbl 07611158 SUT J. Math. 58, No. 1, 77-89 (2022). Reviewer: Lajos Hajdu (Debrecen) MSC: 11D61 PDF BibTeX XML Cite \textit{N. Terai} et al., SUT J. Math. 58, No. 1, 77--89 (2022; Zbl 07611158) Full Text: DOI
Fei, Shuanglin; Luo, Jiagui A note on the exponential Diophantine equation \((rlm^2-1)^x+(r(r-l)m^2+1)^y=(rm)^z\). (English) Zbl 1502.11037 Bull. Braz. Math. Soc. (N.S.) 53, No. 4, 1499-1517 (2022). MSC: 11D61 PDF BibTeX XML Cite \textit{S. Fei} and \textit{J. Luo}, Bull. Braz. Math. Soc. (N.S.) 53, No. 4, 1499--1517 (2022; Zbl 1502.11037) Full Text: DOI
Orosram, Wachirarak; Jaidee, Sawian; Tangjai, Wipawee On the exponential Diophantine equation \((p+2)^x+(2p+1)^y=z^2\), where \(p,p+2\), and \(2p+1\) are primes. (English) Zbl 1513.11109 Int. J. Math. Comput. Sci. 17, No. 4, 1677-1683 (2022). MSC: 11D61 PDF BibTeX XML Cite \textit{W. Orosram} et al., Int. J. Math. Comput. Sci. 17, No. 4, 1677--1683 (2022; Zbl 1513.11109) Full Text: Link
Viriyapong, Nongluk; Viriyapong, Chokchai On the diophantine equation \(n^x+19^y=z^2\), where \(n\equiv 2\pmod{57}\). (English) Zbl 1513.11116 Int. J. Math. Comput. Sci. 17, No. 4, 1639-1642 (2022). MSC: 11D61 PDF BibTeX XML Cite \textit{N. Viriyapong} and \textit{C. Viriyapong}, Int. J. Math. Comput. Sci. 17, No. 4, 1639--1642 (2022; Zbl 1513.11116) Full Text: Link
Pakapongpun, Apisit; Chattae, Bunthita On the diophantine equation \(p^x+7^y=z^2\), where \(p\) is prime and \(x,y,z\) are non-negative integers. (English) Zbl 1513.11110 Int. J. Math. Comput. Sci. 17, No. 4, 1535-1540 (2022). MSC: 11D61 PDF BibTeX XML Cite \textit{A. Pakapongpun} and \textit{B. Chattae}, Int. J. Math. Comput. Sci. 17, No. 4, 1535--1540 (2022; Zbl 1513.11110) Full Text: Link
Tangjai, Wipawee; Chaeoueng, Suveera; Phumchaichot, Naruemon On the diophantine equation \(7^x+5\cdot p^y=z^2\) where \(p\equiv 1,2,4\pmod 7\). (English) Zbl 1513.11113 Int. J. Math. Comput. Sci. 17, No. 4, 1483-1489 (2022). MSC: 11D61 PDF BibTeX XML Cite \textit{W. Tangjai} et al., Int. J. Math. Comput. Sci. 17, No. 4, 1483--1489 (2022; Zbl 1513.11113) Full Text: Link
Aquino, Ronald L.; Bacani, Jerico B. On the exponential Diophantine equation \(p^x+q^y=z^3\): theorems and conjectures. (English) Zbl 1496.11057 Giri, Debasis (ed.) et al., Proceedings of the seventh international conference on mathematics and computing, ICMC 2021, Shibpur, India, March 2–5, 2021. Singapore: Springer. Adv. Intell. Syst. Comput. 1412, 711-723 (2022). MSC: 11D61 PDF BibTeX XML Cite \textit{R. L. Aquino} and \textit{J. B. Bacani}, Adv. Intell. Syst. Comput. 1412, 711--723 (2022; Zbl 1496.11057) Full Text: DOI
Nguyen Xuan Tho A note on the Diophantine equation \((x+1)^3 + (x+2)^3 + \cdots + (2x)^3 = y^n\). (English) Zbl 1510.11090 Elem. Math. 77, No. 3, 142-143 (2022). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11D41 11A05 11A07 11D61 PDF BibTeX XML Cite \textit{Nguyen Xuan Tho}, Elem. Math. 77, No. 3, 142--143 (2022; Zbl 1510.11090) Full Text: DOI
Fujita, Yasutsugu; Le, Maohua A parametric family of ternary purely exponential Diophantine equation \(A^x + B^y = C^z\). (English) Zbl 1517.11026 Turk. J. Math. 46, No. 4, 1224-1232 (2022). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{Y. Fujita} and \textit{M. Le}, Turk. J. Math. 46, No. 4, 1224--1232 (2022; Zbl 1517.11026) Full Text: DOI
Gómez, Carlos Alexis; Gómez, Jhonny Carpediem; Luca, Florian On the exponential Diophantine equation \(F_{n+1}^x - F_{n-1}^x = F_m^y\). (English) Zbl 1497.11083 Taiwanese J. Math. 26, No. 4, 685-712 (2022). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D61 11B39 11J86 PDF BibTeX XML Cite \textit{C. A. Gómez} et al., Taiwanese J. Math. 26, No. 4, 685--712 (2022; Zbl 1497.11083) Full Text: DOI Link
Terai, Nobuhiro; Fujita, Yasutsugu On exponential Diophantine equations concerning Pythagorean triples. (English) Zbl 1513.11114 Publ. Math. Debr. 101, No. 1-2, 147-168 (2022). Reviewer: István Gaál (Debrecen) MSC: 11D61 11D41 11J86 PDF BibTeX XML Cite \textit{N. Terai} and \textit{Y. Fujita}, Publ. Math. Debr. 101, No. 1--2, 147--168 (2022; Zbl 1513.11114) Full Text: DOI
Guo, Xiaoyan; Lei, Deli A note on the Lebesgue-Ljunggren-Nagell equation \(ax^2+b^{2m}=4y^n\). (English) Zbl 1513.11106 Period. Math. Hung. 85, No. 1, 72-80 (2022). MSC: 11D61 PDF BibTeX XML Cite \textit{X. Guo} and \textit{D. Lei}, Period. Math. Hung. 85, No. 1, 72--80 (2022; Zbl 1513.11106) Full Text: DOI
Mutlu, Elif Kızıldere; Le, Maohua; Soydan, Gökhan A modular approach to the generalized Ramanujan-Nagell equation. (English) Zbl 1502.11039 Indag. Math., New Ser. 33, No. 5, 992-1000 (2022). Reviewer: Arman Shamsi Zargar (Ardabil) MSC: 11D61 14H52 PDF BibTeX XML Cite \textit{E. K. Mutlu} et al., Indag. Math., New Ser. 33, No. 5, 992--1000 (2022; Zbl 1502.11039) Full Text: DOI arXiv
Dimitrov, Stoyan Ivanov On a tangent equation by primes. (English) Zbl 1492.11142 Georgian Math. J. 29, No. 4, 493-504 (2022). MSC: 11P55 11L07 PDF BibTeX XML Cite \textit{S. I. Dimitrov}, Georgian Math. J. 29, No. 4, 493--504 (2022; Zbl 1492.11142) Full Text: DOI arXiv
Li, Jinjiang; Zhang, Min; Xue, Fei On a ternary Diophantine equation involving fractional powers with prime variables of a special form. (English) Zbl 1512.11061 Ramanujan J. 58, No. 4, 1171-1199 (2022). Reviewer: Thomas Stoll (Vandœuvre-lès Nancy) MSC: 11L07 11L20 11P05 11P32 11N36 PDF BibTeX XML Cite \textit{J. Li} et al., Ramanujan J. 58, No. 4, 1171--1199 (2022; Zbl 1512.11061) Full Text: DOI
Borah, Padma Bhushan; Dutta, Mridul On the Diophantine equation \(7^x+32^y=z^2\) and its generalization. (English) Zbl 1495.11053 Integers 22, Paper A29, 5 p. (2022). Reviewer: Anitha Srinivasan (Madrid) MSC: 11D61 PDF BibTeX XML Cite \textit{P. B. Borah} and \textit{M. Dutta}, Integers 22, Paper A29, 5 p. (2022; Zbl 1495.11053) Full Text: Link
Nansoko, Souleymane; Tchammou, Euloge; Togbé, A. The Diophantine equation \(\sum_{j=1}^k jF_j^p=L_n^q\). (English) Zbl 1493.11038 Integers 22, Paper A5, 16 p. (2022). MSC: 11B39 11D61 PDF BibTeX XML Cite \textit{S. Nansoko} et al., Integers 22, Paper A5, 16 p. (2022; Zbl 1493.11038) Full Text: Link
Ghadermarzi, Amir On the exceptional solutions of Jeśmanowicz’ conjecture. (English) Zbl 1505.11059 Bull. Iran. Math. Soc. 48, No. 3, 933-949 (2022). Reviewer: Imin Chen (Burnaby) MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{A. Ghadermarzi}, Bull. Iran. Math. Soc. 48, No. 3, 933--949 (2022; Zbl 1505.11059) Full Text: DOI arXiv
Dimitrov, Stoyan I. On an equation with prime numbers close to squares. (English) Zbl 1513.11166 Stud. Sci. Math. Hung. 59, No. 2, 116-123 (2022). Reviewer: Shigeru Kanemitsu (Kitakyushu) MSC: 11P32 11L07 PDF BibTeX XML Cite \textit{S. I. Dimitrov}, Stud. Sci. Math. Hung. 59, No. 2, 116--123 (2022; Zbl 1513.11166) Full Text: DOI arXiv
Miyazaki, Takafumi; Sudo, Masaki; Terai, Nobuhiro A purely exponential Diophantine equation in three unknowns. (English) Zbl 1513.11108 Period. Math. Hung. 84, No. 2, 287-298 (2022). Reviewer: Jan-Hendrik Evertse (Leiden) MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{T. Miyazaki} et al., Period. Math. Hung. 84, No. 2, 287--298 (2022; Zbl 1513.11108) Full Text: DOI
Adédji, K. N.; Filipin, A.; Togbé, A. The extension of the \(D(-k)\)-triple \(\{1,k,k+1\}\) to a quadruple. (English) Zbl 1513.11104 Acta Math. Hung. 166, No. 2, 407-422 (2022). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11D61 11B39 11J86 11Y50 PDF BibTeX XML Cite \textit{K. N. Adédji} et al., Acta Math. Hung. 166, No. 2, 407--422 (2022; Zbl 1513.11104) Full Text: DOI
Şiar, Z.; Keskin, R. On the exponential Diophantine equation \((a^n-2)(b^n-2)=x^2\). (English) Zbl 1496.11058 Math. Notes 111, No. 6, 903-912 (2022). Reviewer: Anitha Srinivasan (Madrid) MSC: 11D61 PDF BibTeX XML Cite \textit{Z. Şiar} and \textit{R. Keskin}, Math. Notes 111, No. 6, 903--912 (2022; Zbl 1496.11058) Full Text: DOI arXiv
Hajdu, L.; Sebestyén, P. Terms of recurrence sequences in the solution sets of generalized Pell equations. (English) Zbl 1501.11045 Int. J. Number Theory 18, No. 7, 1605-1612 (2022). Reviewer: Clemens Fuchs (Salzburg) MSC: 11D09 11D61 11B39 PDF BibTeX XML Cite \textit{L. Hajdu} and \textit{P. Sebestyén}, Int. J. Number Theory 18, No. 7, 1605--1612 (2022; Zbl 1501.11045) Full Text: DOI
Fujita, Yasutsugu; Le, Maohua A note on the number of solutions of the Pillai type equation \(| a^x - b^y | = k\). (English) Zbl 1497.11082 J. Number Theory 239, 40-56 (2022). MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{Y. Fujita} and \textit{M. Le}, J. Number Theory 239, 40--56 (2022; Zbl 1497.11082) Full Text: DOI
Dimitrov, Stoyan Ivanov On an equation by primes with one Linnik prime. (English) Zbl 1487.11079 Georgian Math. J. 29, No. 3, 455-470 (2022). MSC: 11L07 11L20 11P32 PDF BibTeX XML Cite \textit{S. I. Dimitrov}, Georgian Math. J. 29, No. 3, 455--470 (2022; Zbl 1487.11079) Full Text: DOI arXiv
Kreutz, Alessandra; Marques, Diego; Trojovský, Pavel On Fibonacci numbers as sum of powers of two consecutive tribonacci numbers. (English) Zbl 1496.11024 Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 116, No. 3, Paper No. 119, 16 p. (2022). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11B39 11J86 11D61 PDF BibTeX XML Cite \textit{A. Kreutz} et al., Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 116, No. 3, Paper No. 119, 16 p. (2022; Zbl 1496.11024) Full Text: DOI
Saye, Robert I. On two conjectures concerning the ternary digits of powers of two. (English) Zbl 1495.11012 J. Integer Seq. 25, No. 3, Article 22.3.4, 9 p. (2022). MSC: 11A63 11Y55 11D61 11Y50 PDF BibTeX XML Cite \textit{R. I. Saye}, J. Integer Seq. 25, No. 3, Article 22.3.4, 9 p. (2022; Zbl 1495.11012) Full Text: arXiv Link
Boyer, Simon; Robert, Olivier Rational points on an intersection of diagonal forms. (English) Zbl 1505.11131 Acta Arith. 203, No. 2, 165-194 (2022). Reviewer: D. R. Heath-Brown (Oxford) MSC: 11P55 11D72 11D45 11D41 11L07 PDF BibTeX XML Cite \textit{S. Boyer} and \textit{O. Robert}, Acta Arith. 203, No. 2, 165--194 (2022; Zbl 1505.11131) Full Text: DOI arXiv
García, Jonathan; Gómez, Carlos A. On a variant of Pillai problem: integers as difference between generalized Pell numbers and perfect powers. (English) Zbl 1490.11024 Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 116, No. 3, Paper No. 103, 36 p. (2022). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11B39 11D45 11D61 11J86 PDF BibTeX XML Cite \textit{J. García} and \textit{C. A. Gómez}, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 116, No. 3, Paper No. 103, 36 p. (2022; Zbl 1490.11024) Full Text: DOI
Bennett, Michael A.; Gherga, Adela; Patel, Vandita; Siksek, Samir Odd values of the Ramanujan tau function. (English) Zbl 07522777 Math. Ann. 382, No. 1-2, 203-238 (2022). MSC: 11D61 11D41 11F80 11F41 PDF BibTeX XML Cite \textit{M. A. Bennett} et al., Math. Ann. 382, No. 1--2, 203--238 (2022; Zbl 07522777) Full Text: DOI arXiv
Bajpai, Prajeet; Bennett, Michael A. A note on pencils of norm-form equations. (English) Zbl 07517642 Acta Arith. 203, No. 1, 19-26 (2022). Reviewer: Gökhan Soydan (Bursa) MSC: 11D57 11D61 11J86 11R16 PDF BibTeX XML Cite \textit{P. Bajpai} and \textit{M. A. Bennett}, Acta Arith. 203, No. 1, 19--26 (2022; Zbl 07517642) Full Text: DOI arXiv
Balakrishnan, Jennifer S.; Craig, William; Ono, Ken Variations of Lehmer’s conjecture for Ramanujan’s tau-function. (English) Zbl 1497.11080 J. Number Theory 237, 3-14 (2022). Reviewer: Gökhan Soydan (Bursa) MSC: 11D61 11B39 11D41 11J86 PDF BibTeX XML Cite \textit{J. S. Balakrishnan} et al., J. Number Theory 237, 3--14 (2022; Zbl 1497.11080) Full Text: DOI arXiv
Fu, Ruiqin; Yang, Hai On the generalized Ramanujan-Nagell equation \(x^2+(3m^2+1)=(4m^2+1)^n\). (English) Zbl 1492.11075 Indian J. Pure Appl. Math. 53, No. 1, 222-227 (2022). Reviewer: Anitha Srinivasan (Madrid) MSC: 11D61 PDF BibTeX XML Cite \textit{R. Fu} and \textit{H. Yang}, Indian J. Pure Appl. Math. 53, No. 1, 222--227 (2022; Zbl 1492.11075) Full Text: DOI
Terai, Nobuhiro On the Diophantine equation \(x^2+b^m=c^n\) with \(a^2+b^4=c^2\). (English) Zbl 1491.11035 Indian J. Pure Appl. Math. 53, No. 1, 162-169 (2022). Reviewer: Ilker Inam (Bilecik) MSC: 11D61 PDF BibTeX XML Cite \textit{N. Terai}, Indian J. Pure Appl. Math. 53, No. 1, 162--169 (2022; Zbl 1491.11035) Full Text: DOI
Özman, Ekin; Siksek, Samir S-unit equations and the asymptotic Fermat conjecture over number fields. (English) Zbl 1514.11024 Kurşungöz, Kağan (ed.) et al., Number theory. Proceedings of the Journées Arithmétiques, 2019, XXXI, Istanbul University, Turkey, July 1–5, 2019. Berlin: De Gruyter. De Gruyter Proc. Math., 83-103 (2022). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11D41 11G05 11D61 PDF BibTeX XML Cite \textit{E. Özman} and \textit{S. Siksek}, in: Number theory. Proceedings of the Journées Arithmétiques, 2019, XXXI, Istanbul University, Turkey, July 1--5, 2019. Berlin: De Gruyter. 83--103 (2022; Zbl 1514.11024) Full Text: DOI arXiv
Fujita, Yasutsugu; Le, Maohua Some exponential Diophantine equations. II: The equation \(x^2 - dy^2=k^z\) for even \(k\). (English) Zbl 1491.11034 Math. Slovaca 72, No. 2, 341-354 (2022). MSC: 11D61 PDF BibTeX XML Cite \textit{Y. Fujita} and \textit{M. Le}, Math. Slovaca 72, No. 2, 341--354 (2022; Zbl 1491.11034) Full Text: DOI
Baker, Alan [Masser, David] Transcendental number theory. With a new foreword by David Masser. Reprint of the 1990 paperback edition. (English) Zbl 1496.11001 Cambridge Mathematical Library. Cambridge: Cambridge University Press (ISBN 978-1-00-922994-4/pbk; 978-1-00-922993-7/ebook). xiv, 169 p. (2022). MSC: 11-01 01A75 11J81 11J86 11J85 11J89 11J83 11J68 11D41 11J91 11R29 11K60 11R11 PDF BibTeX XML Cite \textit{A. Baker}, Transcendental number theory. With a new foreword by David Masser. Reprint of the 1990 paperback edition. Cambridge: Cambridge University Press (2022; Zbl 1496.11001) Full Text: DOI
Das, Pranabesh; Dey, Pallab Kanti; Koutsianas, Angelos; Tzanakis, Nikos Perfect powers in sum of three fifth powers. (English) Zbl 1493.11073 J. Number Theory 236, 443-462 (2022). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11D61 11D41 11F11 11F80 PDF BibTeX XML Cite \textit{P. Das} et al., J. Number Theory 236, 443--462 (2022; Zbl 1493.11073) Full Text: DOI arXiv
Pakapongpun, Apisit; Chattae, Bunthita On the diophantine equation \(a^x+(a+2)^y=z^2\), where \(a \equiv 3 \pmod{20}\). (English) Zbl 1492.11076 Int. J. Math. Comput. Sci. 17, No. 2, 711-716 (2022). MSC: 11D61 PDF BibTeX XML Cite \textit{A. Pakapongpun} and \textit{B. Chattae}, Int. J. Math. Comput. Sci. 17, No. 2, 711--716 (2022; Zbl 1492.11076) Full Text: Link
Orosram, Wachirarak; Unchai, Ariya On the diophantine equation \(2^{2nx}-p^y=z^2\), where \(p\) is a prime. (English) Zbl 1499.11173 Int. J. Math. Comput. Sci. 17, No. 1, 447-451 (2022). MSC: 11D61 PDF BibTeX XML Cite \textit{W. Orosram} and \textit{A. Unchai}, Int. J. Math. Comput. Sci. 17, No. 1, 447--451 (2022; Zbl 1499.11173) Full Text: Link
Alabbood, Mohammed A. On some exponential Diophantine equations. (English) Zbl 1499.11169 Int. J. Math. Comput. Sci. 17, No. 1, 431-438 (2022). MSC: 11D61 PDF BibTeX XML Cite \textit{M. A. Alabbood}, Int. J. Math. Comput. Sci. 17, No. 1, 431--438 (2022; Zbl 1499.11169) Full Text: Link
Yang, Hai; Fu, Ruiqin A further note on Jeśmanowicz’ conjecture concerning primitive Pythagorean triples. (English) Zbl 1495.11054 Mediterr. J. Math. 19, No. 2, Paper No. 57, 8 p. (2022). MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{H. Yang} and \textit{R. Fu}, Mediterr. J. Math. 19, No. 2, Paper No. 57, 8 p. (2022; Zbl 1495.11054) Full Text: DOI
Koymans, Peter The generalized Catalan equation in positive characteristic. (English) Zbl 1500.11030 Int. J. Number Theory 18, No. 2, 269-276 (2022). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D61 11G30 PDF BibTeX XML Cite \textit{P. Koymans}, Int. J. Number Theory 18, No. 2, 269--276 (2022; Zbl 1500.11030) Full Text: DOI arXiv
Alahmadi, Adel; Luca, Florian On the Euler function of \(Y\)-coordinates of Pell equations and repdigits. (English) Zbl 1485.11073 Result. Math. 77, No. 2, Paper No. 59, 6 p. (2022). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11D61 11A25 11B39 11A63 PDF BibTeX XML Cite \textit{A. Alahmadi} and \textit{F. Luca}, Result. Math. 77, No. 2, Paper No. 59, 6 p. (2022; Zbl 1485.11073) Full Text: DOI
Chałupka, Karolina; Dąbrowski, Andrzej; Soydan, Gökhan On a class of generalized Fermat equations of signature \((2,2n,3)\). (English) Zbl 1505.11058 J. Number Theory 234, 153-178 (2022). Reviewer: Imin Chen (Burnaby) MSC: 11D61 11B39 PDF BibTeX XML Cite \textit{K. Chałupka} et al., J. Number Theory 234, 153--178 (2022; Zbl 1505.11058) Full Text: DOI arXiv
Nguyen Xuan Tho Solutions to a Lebesgue-Nagell equation. (English) Zbl 1486.11052 Bull. Aust. Math. Soc. 105, No. 1, 19-30 (2022). Reviewer: Ismail Naci Cangül (Bursa) MSC: 11D61 11D72 11B39 PDF BibTeX XML Cite \textit{Nguyen Xuan Tho}, Bull. Aust. Math. Soc. 105, No. 1, 19--30 (2022; Zbl 1486.11052) Full Text: DOI
Chakraborty, Kalyan; Hoque, Azizul On the Diophantine equation \(dx^2+p^{2a}q^{2b}=4y^p\). (English) Zbl 1490.11041 Result. Math. 77, No. 1, Paper No. 18, 11 p. (2022). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11D61 11D41 11Y50 PDF BibTeX XML Cite \textit{K. Chakraborty} and \textit{A. Hoque}, Result. Math. 77, No. 1, Paper No. 18, 11 p. (2022; Zbl 1490.11041) Full Text: DOI arXiv
Kızıldere, Elif; Soydan, Gökhan; Han, Qing; Yuan, Pingzhi The shuffle variant of a Diophantine equation of Miyazaki and Togbé. (English) Zbl 07691444 Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 64(112), No. 3, 243-254 (2021). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11D61 11D41 11J86 PDF BibTeX XML Cite \textit{E. Kızıldere} et al., Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 64(112), No. 3, 243--254 (2021; Zbl 07691444) Full Text: arXiv
Bérczes, Attila; Le, Maohua; Pink, István; Soydan, Gökhan A note on the ternary Diophantine equation \(x^2-y^{2m}=z^n\). (English) Zbl 07660045 An. Științ. Univ. “Ovidius” Constanța, Ser. Mat. 29, No. 2, 93-105 (2021). MSC: 11D41 11D61 PDF BibTeX XML Cite \textit{A. Bérczes} et al., An. Științ. Univ. ``Ovidius'' Constanța, Ser. Mat. 29, No. 2, 93--105 (2021; Zbl 07660045) Full Text: DOI
Leonetti, Paolo On consecutive perfect powers with elementary methods. (English) Zbl 07620506 Nathanson, Melvyn B. (ed.), Combinatorial and additive number theory IV. Selected papers based on the presentations at the CANT 2019 and 2020 workshops, New York, NY, USA, May 21–24, 2019 and virtual, June 1–5, 2020. Cham: Springer. Springer Proc. Math. Stat. 347, 385-400 (2021). Reviewer: Gökhan Soydan (Bursa) MSC: 11D61 11D41 PDF BibTeX XML Cite \textit{P. Leonetti}, Springer Proc. Math. Stat. 347, 385--400 (2021; Zbl 07620506) Full Text: DOI arXiv
Luo, Jiagui Perfect powers of five with few ternary digits. (Chinese. English summary) Zbl 1513.11102 Chin. Ann. Math., Ser. A 42, No. 4, 359-378 (2021). MSC: 11D41 11D61 PDF BibTeX XML Cite \textit{J. Luo}, Chin. Ann. Math., Ser. A 42, No. 4, 359--378 (2021; Zbl 1513.11102) Full Text: DOI
Cantone, Domenico; Omodeo, Eugenio G. “One equation to rule them all”, revisited. (English) Zbl 07552287 Rend. Ist. Mat. Univ. Trieste 53, Paper No. 28, 32 p. (2021). MSC: 03D25 11D25 PDF BibTeX XML Cite \textit{D. Cantone} and \textit{E. G. Omodeo}, Rend. Ist. Mat. Univ. Trieste 53, Paper No. 28, 32 p. (2021; Zbl 07552287) Full Text: DOI
Yu, Yahui; Hu, Jiayuan On the generalized Ramanujan-nagell equation \(x^2+(2k-1)^y = k^z\) with \(k\equiv 3 \pmod 4\). (English) Zbl 07536351 AIMS Math. 6, No. 10, 10596-10601 (2021). MSC: 11D61 PDF BibTeX XML Cite \textit{Y. Yu} and \textit{J. Hu}, AIMS Math. 6, No. 10, 10596--10601 (2021; Zbl 07536351) Full Text: DOI
Huang, Jing; Han, Ao; Liu, Huafeng On a Diophantine equation with prime variables. (English) Zbl 07536295 AIMS Math. 6, No. 9, 9602-9618 (2021). MSC: 11J25 11L03 11P32 PDF BibTeX XML Cite \textit{J. Huang} et al., AIMS Math. 6, No. 9, 9602--9618 (2021; Zbl 07536295) Full Text: DOI
Seayap, Chaiya Some properties of nonlinear general Diophantine equation \((4n-1)^x + 17^y = z^2\). (English) Zbl 1499.11174 JP J. Algebra Number Theory Appl. 52, No. 1, 115-125 (2021). MSC: 11D61 PDF BibTeX XML Cite \textit{C. Seayap}, JP J. Algebra Number Theory Appl. 52, No. 1, 115--125 (2021; Zbl 1499.11174) Full Text: DOI
Zhang, Zhongfeng; Togbé, Alain On the Ramanujan-Nagell type Diophantine equation \(Dx^2+k^n=B\). (English) Zbl 1493.11071 Glas. Mat., III. Ser. 56, No. 2, 263-270 (2021). Reviewer: Maciej Ulas (Kraków) MSC: 11D41 11D61 PDF BibTeX XML Cite \textit{Z. Zhang} and \textit{A. Togbé}, Glas. Mat., III. Ser. 56, No. 2, 263--270 (2021; Zbl 1493.11071) Full Text: DOI
Yamada, Tomohiro An exponential Diophantine equation related to odd perfect numbers. (English) Zbl 1491.11036 Acta Math. Univ. Comen., New Ser. 90, No. 2, 145-155 (2021). Reviewer: Gökhan Soydan (Bursa) MSC: 11D61 11A25 11J86 11D45 PDF BibTeX XML Cite \textit{T. Yamada}, Acta Math. Univ. Comen., New Ser. 90, No. 2, 145--155 (2021; Zbl 1491.11036) Full Text: arXiv Link
Guan, Xungui A conjecture of Jeśmanowicz concerning Pythagorean triples. (Chinese. English summary) Zbl 1488.11092 Adv. Math., Beijing 50, No. 4, 519-528 (2021). MSC: 11D61 PDF BibTeX XML Cite \textit{X. Guan}, Adv. Math., Beijing 50, No. 4, 519--528 (2021; Zbl 1488.11092)
Cantone, D.; Casagrande, A.; Fabris, F.; Omodeo, E. The quest for Diophantine finite-fold-Ness. (English) Zbl 07446605 Matematiche 76, No. 1, 133-160 (2021). MSC: 03D25 03D35 PDF BibTeX XML Cite \textit{D. Cantone} et al., Matematiche 76, No. 1, 133--160 (2021; Zbl 07446605) Full Text: DOI
Patel, Vandita A Lucas-Lehmer approach to generalised Lebesgue-Ramanujan-Nagell equations. (English) Zbl 1484.11102 Ramanujan J. 56, No. 2, 585-596 (2021). Reviewer: Florian Luca (Johannesburg) MSC: 11D61 11D41 11D59 PDF BibTeX XML Cite \textit{V. Patel}, Ramanujan J. 56, No. 2, 585--596 (2021; Zbl 1484.11102) Full Text: DOI arXiv
Le, Maohua; Soydan, Gökhan A note on Terai’s conjecture concerning primitive Pythagorean triples. (English) Zbl 1488.11093 Hacet. J. Math. Stat. 50, No. 4, 911-917 (2021). MSC: 11D61 PDF BibTeX XML Cite \textit{M. Le} and \textit{G. Soydan}, Hacet. J. Math. Stat. 50, No. 4, 911--917 (2021; Zbl 1488.11093) Full Text: DOI
Kihel, Omar; Larone, Jesse On the nonnegative integer solutions of the equation \(F_n \pm F_m = y^a\). (English) Zbl 1486.11020 Quaest. Math. 44, No. 8, 1133-1139 (2021). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11B39 11J86 11D61 PDF BibTeX XML Cite \textit{O. Kihel} and \textit{J. Larone}, Quaest. Math. 44, No. 8, 1133--1139 (2021; Zbl 1486.11020) Full Text: DOI
Fujita, Yasutsugu; Le, Maohua Dem’janenko’s theorem on Jeśmanowicz’ conjecture concerning Pythagorean triples revisited. (English) Zbl 1497.11081 Bull. Malays. Math. Sci. Soc. (2) 44, No. 6, 4059-4083 (2021). MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{Y. Fujita} and \textit{M. Le}, Bull. Malays. Math. Sci. Soc. (2) 44, No. 6, 4059--4083 (2021; Zbl 1497.11081) Full Text: DOI
Koutsianas, Angelos On the solutions of the Diophantine equation \((x-d)^2 +x^2 +(x+d)^2 =y^n\) for \(d\) a prime power. (English) Zbl 1505.11060 Funct. Approximatio, Comment. Math. 64, No. 2, 141-151 (2021). Reviewer: Gökhan Soydan (Bursa) MSC: 11D61 PDF BibTeX XML Cite \textit{A. Koutsianas}, Funct. Approximatio, Comment. Math. 64, No. 2, 141--151 (2021; Zbl 1505.11060) Full Text: DOI arXiv
Erazo, Harold S.; Gómez, Carlos A.; Luca, Florian On Pillai’s problem with \(X\)-coordinates of Pell equations and powers of 2. II. (English) Zbl 1493.11074 Int. J. Number Theory 17, No. 10, 2251-2277 (2021). Reviewer: Ilker Inam (Bilecik) MSC: 11D61 11B39 11D45 PDF BibTeX XML Cite \textit{H. S. Erazo} et al., Int. J. Number Theory 17, No. 10, 2251--2277 (2021; Zbl 1493.11074) Full Text: DOI
Godinho, Hemar; Neumann, Victor G. L. The Diophantine equation \(x^2+ p^a q^b= y^q\). (English) Zbl 1486.11051 Int. J. Number Theory 17, No. 9, 2113-2130 (2021). Reviewer: Ismail Naci Cangül (Bursa) MSC: 11D61 11D41 11D45 PDF BibTeX XML Cite \textit{H. Godinho} and \textit{V. G. L. Neumann}, Int. J. Number Theory 17, No. 9, 2113--2130 (2021; Zbl 1486.11051) Full Text: DOI
Deng, Naijuan Number of solutions to \({(an)^x} + {(bn)^y} = {(cn)^z}\). (Chinese. English summary) Zbl 1488.11091 Math. Pract. Theory 51, No. 9, 194-204 (2021). MSC: 11D61 PDF BibTeX XML Cite \textit{N. Deng}, Math. Pract. Theory 51, No. 9, 194--204 (2021; Zbl 1488.11091)
Luo, Jiagui; Fei, Shuanglin; Li, Yuan On some equations related to Ma’s conjecture. (Chinese. English summary) Zbl 1488.11086 Chin. Ann. Math., Ser. A 42, No. 2, 229-236 (2021). MSC: 11D41 11D61 PDF BibTeX XML Cite \textit{J. Luo} et al., Chin. Ann. Math., Ser. A 42, No. 2, 229--236 (2021; Zbl 1488.11086) Full Text: DOI
Tong, Ruizhou On the Diophantine equation \((2^x-1)(p^y-1)=2z^2\). (English) Zbl 1513.11115 Czech. Math. J. 71, No. 3, 689-696 (2021). MSC: 11D61 PDF BibTeX XML Cite \textit{R. Tong}, Czech. Math. J. 71, No. 3, 689--696 (2021; Zbl 1513.11115) Full Text: DOI