Prugsapitak, Supawadee; Sangjan, Phitchayawee On the Diophantine equation of the form \(4^{x'}+(m^2-1)^x=y^2\). (English) Zbl 07907979 Int. J. Math. Comput. Sci. 20, No. 1, 187-190 (2025). MSC: 11D61 11D99 × Cite Format Result Cite Review PDF Full Text: DOI
Dokchan, Rakporn; Panngam, Nopparat On the Diophantine equation \(a^x+(a+5b)^y=z^2\). (English) Zbl 07907961 Int. J. Math. Comput. Sci. 20, No. 1, 63-66 (2025). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: DOI
Panraksa, Chatchawan A note on the exponential Diophantine equation \(8^x+161^y=z^2\). (English) Zbl 07907957 Int. J. Math. Comput. Sci. 20, No. 1, 41-43 (2025). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: DOI
Ouzahra, Mohamed On the finiteness of solutions for certain Diophantine equations. (English) Zbl 07920329 Ramanujan J. 65, No. 1, 263-275 (2024). MSC: 11D72 05A16 11D61 × Cite Format Result Cite Review PDF Full Text: DOI
Coppola, Nirvana; Curcó-Iranzo, Mar; Khawaja, Maleeha; Patel, Vandita; Ülkem, Özge Power values of power sums: a survey. (English) Zbl 07919515 Abdellatif, Ramla (ed.) et al., Women in numbers Europe IV. Research directions in number theory. Selected papers based on the presentations at the 4th workshop, WINE 4, Utrecht, the Netherlands, August 29 – September 2, 2022. Cham: Springer. Assoc. Women Math. Ser. 32, 155-193 (2024). MSC: 11D61 11D41 11D25 11F80 11G05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Phosri, Piyada; Tadee, Suton On the Diophantine equations \(q^x + p(2q + 1)^y = z^2\) and \(q^x + p(4q + 1)^y = z^2\). (English) Zbl 07916021 Thai J. Math. 22, No. 2, 389-395 (2024). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Chakraborty, Kalyan; Hoque, Azizul On the exponential Diophantine equation \(x^2+p^m q^n=2y^p\). (English) Zbl 07905784 N. Z. J. Math. 55, 53-60 (2024). MSC: 11D61 11D41 11Y50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Li, Yuan; Zhang, Jing; Liu, Baoxing On equations \((-1)^\alpha p^x+ (-1)^\beta (2^k(2p + 1))^y= z^2\) with Sophie Germain prime \(p\). (English) Zbl 07904869 Involve 17, No. 3, 503-518 (2024). MSC: 11A15 11D61 11D72 14H52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bajpai, Prajeet; Bennett, Michael A. Effective \(S\)-unit equations beyond three terms: Newman’s conjecture. (English) Zbl 07903826 Acta Arith. 214, 421-458 (2024). MSC: 11D61 11D45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Erduvan, F.; Keskin, R. Balancing numbers which are concatenations of three repdigits. (English) Zbl 07898624 Carpathian Math. Publ. 16, No. 1, 148-157 (2024). MSC: 11B39 11J86 11D61 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Baruah, Priyanka; Das, Anup; Hoque, Azizul Complete solutions of a Lebesgue-Ramanujan-Nagell type equation. (English) Zbl 07893344 Arch. Math. (Brno) 60, No. 3, 135-144 (2024). MSC: 11D61 11D41 11Y50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ameur, Zahra; Boumahdi, Rachid; Garici, Tarek Some results concerning the exponential Diophantine equation \((a^n-1)(b^m-1) = x^2\). (English) Zbl 07881005 Indian J. Pure Appl. Math. 55, No. 2, 613-622 (2024). MSC: 11D41 11D61 × Cite Format Result Cite Review PDF Full Text: DOI
Hoque, Azizul On a class of Lebesgue-Ramanujan-Nagell equations. (English) Zbl 07880178 Period. Math. Hung. 88, No. 2, 418-428 (2024). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11D61 11D41 11B39 11Y50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fujita, Yasutsugu; Le, Maohua A note on the Goormaghtigh equation concerning difference sets. (English) Zbl 07873466 Bull. Aust. Math. Soc. 109, No. 3, 443-452 (2024). MSC: 11D61 05B10 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Coppola, Nirvana; Curcó-Iranzo, Mar; Khawaja, Maleeha; Patel, Vandita; Ülkem, Özge On perfect powers that are sums of cubes of a nine term arithmetic progression. (English) Zbl 07869080 Indag. Math., New Ser. 35, No. 3, 500-515 (2024). MSC: 11D61 11D41 11D25 14G05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Vukusic, Ingrid; Ziegler, Volker On sums of two Fibonacci numbers that are powers of numbers with limited Hamming weight. (English) Zbl 07868213 Quaest. Math. 47, No. 4, 851-869 (2024). Reviewer: Florian Luca (Johannesburg) MSC: 11B39 11D61 11J86 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Taclay, Richard J. Sum and difference of powers of two Fibonacci numbers. (English) Zbl 07866762 Int. J. Math. Comput. Sci. 19, No. 4, 1155-1158 (2024). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Gayo, William S. jun.; Siong, Venus D. Unsolvability of two diophantine equations of the form \(p^a+(p-1)^b=c^2\). (English) Zbl 07866760 Int. J. Math. Comput. Sci. 19, No. 4, 1143-1145 (2024). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Manikandan, K.; Venkatraman, R. On the exponential Diophantine equation \(8^x+161^y=z^2\). (English) Zbl 07866753 Int. J. Math. Comput. Sci. 19, No. 4, 1101-1104 (2024). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Bérczes, Attila; Pink, István; Young, Paul Thomas Cullen numbers and Woodall numbers in generalized Fibonacci sequences. (English) Zbl 07865940 J. Number Theory 262, 86-102 (2024). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D41 11D61 11B39 11S80 × Cite Format Result Cite Review PDF Full Text: DOI
Mutlu, Elif Kızıldere; Soydan, Gökhan On the solutions of some Lebesgue-Ramanujan-Nagell type equations. (English) Zbl 07864365 Int. J. Number Theory 20, No. 5, 1195-1218 (2024). MSC: 11D41 11D61 × Cite Format Result Cite Review PDF Full Text: DOI
N., Malavika; Venkatraman, R. On the exponential Diophantine equation \(3^x+121^y=z^2\). (English) Zbl 07846073 Int. J. Math. Comput. Sci. 19, No. 3, 917-920 (2024). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Taclay, Richard J. On the Diophantine equation \(F^x_n+F^x_{n+1}=y^2\). (English) Zbl 07846050 Int. J. Math. Comput. Sci. 19, No. 3, 721-724 (2024). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Siraworakun, Apirat; Tadee, Suton All solutions of the Diophantine equation \(25^x-7^y=z^2\). (English) Zbl 07846037 Int. J. Math. Comput. Sci. 19, No. 3, 631-633 (2024). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Tadee, Suton The solutions of the Diophantine equations \(p^x+p^y=z^q\) and \(p^x-p^y=z^q\). (English) Zbl 07846035 Int. J. Math. Comput. Sci. 19, No. 3, 621-623 (2024). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Taher, Hunar Sherzad; Dash, Saroj Kumar On the square of Fibonacci and Lucas numbers of the form \((2^{2s}-1)^x+(2^{s+1})^y\). (English) Zbl 07846028 Int. J. Math. Comput. Sci. 19, No. 3, 553-560 (2024). MSC: 11D61 11D45 11B39 × Cite Format Result Cite Review PDF Full Text: Link
Győry, Kálmán; Pethő, Attila; Szalay, László Decomposable forms generated by linear recurrences. (English) Zbl 07842618 J. Integer Seq. 27, No. 3, Article 24.3.5, 20 p. (2024). Reviewer: Clemens Fuchs (Salzburg) MSC: 11B37 11D61 11D72 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Gómez, Carlos A.; Gómez, Jhonny C.; Luca, Florian A Diophantine equation with powers of three consecutive \(k\)-Fibonacci numbers. (English) Zbl 1539.11033 Result. Math. 79, No. 4, Paper No. 136, 21 p. (2024). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11B39 11D61 11J86 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Le, Maohua; Soydan, Gökhan Some exponential Diophantine equations. III: A new look at the generalized Lebesgue-Nagell equation. (English) Zbl 07837711 Bol. Soc. Mat. Mex., III. Ser. 30, No. 2, Paper No. 35, 9 p. (2024). Reviewer: Roberto Amato (Messina) MSC: 11D61 11E16 × Cite Format Result Cite Review PDF Full Text: DOI
Miyazaki, Takafumi; Pink, István Number of solutions to a special type of unit equations in two unknowns. II. (English) Zbl 07837203 Res. Number Theory 10, No. 2, Paper No. 36, 41 p. (2024). MSC: 11D61 11J86 11J61 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Miyazaki, Takafumi; Pink, István Number of solutions to a special type of unit equations in two unknowns. (English) Zbl 07835485 Am. J. Math. 146, No. 2, 295-369 (2024). Reviewer: Florian Luca (Johannesburg) MSC: 11D61 11D41 11D57 11G05 11J86 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mutlu, Elif Kızıldere; Le, Maohua; Soydan, Gökhan An elementary approach to the generalized Ramanujan-Nagell equation. (English) Zbl 07833746 Indian J. Pure Appl. Math. 55, No. 1, 392-399 (2024). Reviewer: Ingrid Vukusic (Salzburg) MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rayaguru, Sai Gopal On the Diophantine equation \(x^2 + C = y^n\). (English) Zbl 1540.11024 Indian J. Pure Appl. Math. 55, No. 1, 69-77 (2024). Reviewer: Seyran S. İbrahimov (Famagusta) MSC: 11D61 11D41 × Cite Format Result Cite Review PDF Full Text: DOI
Santicola, Katerina Reverse engineered Diophantine equations over \(\mathbb{Q}\). (English. French summary) Zbl 07824612 J. Théor. Nombres Bordx. 35, No. 3, 897-904 (2024). MSC: 11D41 11D61 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hajdu, Lajos; Sebestyén, Péter Terms of recurrence sequences in the solution sets of norm form equations. (English) Zbl 1539.11029 Arch. Math. 122, No. 2, 179-187 (2024). Reviewer: Clemens Fuchs (Salzburg) MSC: 11B37 11D57 11D61 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Gómez, Carlos A.; Gómez, Jhonny C.; Luca, Florian The complete solution of the Diophantine equation \(\left(F_{n+1}^{(k)}\right)^x - \left(F_{n-1}^{(k)}\right)^x = F_m^{(k)}\). (English) Zbl 1534.11022 Mediterr. J. Math. 21, No. 1, Paper No. 13, 25 p. (2024). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11B39 11D61 11J86 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Tadee, Suton; Wannaphan, Chantana On the Diophantine equations \((p+a)^x-p^y=z^2\) and \(p^x-(p+a)^y=z^2\). (English) Zbl 1538.11112 Int. J. Math. Comput. Sci. 19, No. 2, 459-465 (2024). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Viriyapong, Chokchai; Viriyapong, Nongluk On the Diophantine equation \(a^x+(a+2)^y=z^2\) where \(a\) is congruent to 19 modulo 28. (English) Zbl 1538.11116 Int. J. Math. Comput. Sci. 19, No. 2, 449-451 (2024). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Viriyapong, Nongluk; Viriyapong, Chokchai On the Diophantine equation \(147^x+741^y=z^2\). (English) Zbl 1538.11117 Int. J. Math. Comput. Sci. 19, No. 2, 445-447 (2024). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Tadee, Suton On the positive integer solutions of \(p^x+p^y=z^2\) in the Fibonacci and Lucas numbers, where \(p\) is prime. (English) Zbl 1538.11111 Int. J. Math. Comput. Sci. 19, No. 2, 377-380 (2024). MSC: 11D61 11B39 × Cite Format Result Cite Review PDF Full Text: Link
Thongnak, Sutthiwat; Kaewong, Theeradach; Chuayjan, Wariam On the exponential Diophantine equation \(11^x-17^y=z^2\). (English) Zbl 1538.11114 Int. J. Math. Comput. Sci. 19, No. 1, 181-184 (2024). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Thongnak, Sutthiwat; Kaewong, Theeradach; Chuayjan, Wariam On the exponential Diophantine equation \(5^x - 3^y = z^2\). (English) Zbl 1538.11113 Int. J. Math. Comput. Sci. 19, No. 1, 99-102 (2024). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Muthuvel, S.; Venkatraman, R. An Exponential Diophantine equation \(x^2+3^{\alpha} 113^{\beta}=y^{\mathfrak{n}}\). arXiv:2405.09252 Preprint, arXiv:2405.09252 [math.NT] (2024). MSC: 11D41 11D61 11Y50 × Cite Format Result Cite Full Text: arXiv OA License
García, Pedro-José Cazorla Asymptotic Fermat’s Last Theorem for a family of equations of signature \((2, 2n, n)\). arXiv:2404.14098 Preprint, arXiv:2404.14098 [math.NT] (2024). MSC: 11D61 11D41 11F80 11F11 × Cite Format Result Cite Full Text: DOI arXiv OA License
Ghosh, Arkabrata WITHDRAWN: Solution of the Diophantine equation \(x^2 + p^k=y^n\). arXiv:2402.19445 Preprint, arXiv:2402.19445 [math.NT] (2024); retraction notice ibid. MSC: 11D41 11D61 × Cite Format Result Cite Full Text: arXiv OA License
Tadee, Suton; Pintoptang, Umarin On the non-linear Diophantine equations \(4^x - a^y = dz^2\) and \(4^x + a^y = dz^2\). (English) Zbl 07829209 Thai J. Math. 21, No. 3, 563-567 (2023). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Şiar, Z.; Keskin, R. On perfect powers in \(k\)-generalized Pell-Lucas sequence. (English) Zbl 07820467 Math. Notes 114, No. 5, 936-948 (2023). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11B39 11J86 11D61 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hamtat, Abdelkader An exponential Diophantine equation on triangular numbers. (English) Zbl 07811077 Math. Appl. (Warsaw) 51, No. 1, 99-107 (2023). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: DOI
Şiar, Zafer; Keskin, Refik; Öztaş, Elif Segah On perfect powers in \(k\)-generalized Pell sequence. (English) Zbl 07790600 Math. Bohem. 148, No. 4, 507-518 (2023). MSC: 11B39 11D61 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Asthana, Shivangi; Singh, M. M. On the Diophantine equations \(x^2 + 139^m =y^n\) and \(x^2 +499^m =y^n\). (English) Zbl 1538.11100 Jñānābha 53, No. 1, 207-211 (2023). MSC: 11D41 11D61 × Cite Format Result Cite Review PDF Full Text: DOI
Fujita, Yasutsugu; Le, Maohua; Terai, Nobuhiro A note on the ternary purely exponential Diophantine equation \(f^x + (f + g)^y = g^z\). (English) Zbl 1534.11046 Tsukuba J. Math. 47, No. 1, 113-123 (2023). MSC: 11D61 11J86 × Cite Format Result Cite Review PDF Full Text: DOI Link
Bennett, Michael A.; Siksek, Samir Differences between perfect powers: prime power gaps. (English) Zbl 1539.11063 Algebra Number Theory 17, No. 10, 1789-1846 (2023). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11D61 11D41 11F80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Fujita, Yasutsugu; Le, Maohua; Terai, Nobuhiro A note on the solution to the generalized Ramanujan-Nagell equation \(x^2+(4c)^y=(c+1)^z\). (English) Zbl 1532.11048 Indian J. Pure Appl. Math. 54, No. 4, 1145-1157 (2023). Reviewer: Ingrid Vukusic (Salzburg) MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: DOI
Tyszka, Apoloniusz A common approach to three open problems in number theory. (English) Zbl 1538.11115 DML, Discrete Math. Lett. 12, 66-72 (2023); correction ibid. 12, 103 (2023). MSC: 11D61 11D85 11Y50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Bugeaud, Yann \(B'\). (English) Zbl 07773867 Publ. Math. Debr. 103, No. 3-4, 499-533 (2023). MSC: 11J86 11J04 11D59 11D61 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Edjeou, Bilizimbéyé; Faye, Bernadette Pell and Pell-Lucas numbers as difference of two repdigits. (English) Zbl 1538.11041 Afr. Mat. 34, No. 4, Paper No. 70, 13 p. (2023). MSC: 11B39 11D61 11D45 11J86 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Irmak, Nurettin A generalization of the equation \((2^k - 1) (3^l - 1) = 5^m - 1\). (English) Zbl 1540.11023 Quaest. Math. 46, No. 12, 2563-2575 (2023). MSC: 11D61 11J86 11B39 × Cite Format Result Cite Review PDF Full Text: DOI
Le, Maohua; Soydan, Gökhan On the ternary purely exponential Diophantine equation \((ak)^x + (bk)^y = ((a + b)k)^z\) for prime powers \(a\) and \(b\). (English) Zbl 1529.11057 J. Integer Seq. 26, No. 7, Article 23.7.8, 18 p. (2023). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D61 11B39 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Bennett, Michael A.; Michaud-Jacobs, Philippe; Siksek, Samir \(\mathbb{Q}\)-curves and the Lebesgue-Nagell equation. (English. French summary) Zbl 07750329 J. Théor. Nombres Bordx. 35, No. 2, 495-510 (2023). MSC: 11D41 11D61 11F80 11G05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Le, Maohua; Styer, Robert On a conjecture concerning the number of solutions to \(a^x+b^y=c^z\). (English) Zbl 1530.11035 Bull. Aust. Math. Soc. 108, No. 1, 40-49 (2023). MSC: 11D61 11D45 × Cite Format Result Cite Review PDF Full Text: DOI
Ray, Anwesh Remarks on Catalan’s equation over function fields. (English) Zbl 07732858 Finite Fields Appl. 91, Article ID 102271, 7 p. (2023). Reviewer: Azizul Hoque (Allahabad) MSC: 11D61 11R58 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
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). Reviewer: Gökhan Soydan (Bursa) MSC: 11D41 11D59 11D61 14G99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Heintze, Sebastian; Tichy, Robert F.; Vukusic, Ingrid; Ziegler, Volker On the Diophantine equation \(U_n - b^m = c\). (English) Zbl 1537.11144 Math. Comput. 92, No. 344, 2825-2859 (2023). Reviewer: István Gaál (Debrecen) MSC: 11Y50 11D61 11B37 11J86 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Das, Pranabesh; Laishram, Shanta; Saradha, N.; Sharma, Divyum Rational solutions to the variants of Erdős-Selfridge superelliptic curves. (English) Zbl 1530.11034 Int. J. Number Theory 19, No. 7, 1707-1744 (2023). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11D61 11D41 11Y50 11G05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tadee, Suton; Thaneepoon, Nuanchuen On the Diophantine equation \(6^x+p^y=z^2\), where \(p\) is prime. (English) Zbl 1524.11088 Int. J. Math. Comput. Sci. 18, No. 4, 737-741 (2023). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Luca, Florian; Zottor, Faith S. On \(Y\)-coordinates of Pell equations which are Fibonacci numbers. (English) Zbl 1527.11028 Bol. Soc. Mat. Mex., III. Ser. 29, No. 2, Paper No. 49, 43 p. (2023). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D61 11B39 11D45 × Cite Format Result Cite Review PDF Full Text: DOI OA License
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 1524.11093 Thai J. Math. 21, No. 1, 67-75 (2023). MSC: 11D72 11D61 11G05 11A15 × Cite Format Result Cite Review PDF Full Text: Link
Kitayama, Hidetaka; Tagawa, Hiroyuki; Urahashi, Keiichi Jeśmanowicz’ conjecture for non-primitive Pythagorean triples. (English) Zbl 1538.11091 Period. Math. Hung. 86, No. 2, 442-453 (2023). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11D09 11D41 11D61 × Cite Format Result Cite Review PDF 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 1538.11060 Period. Math. Hung. 86, No. 2, 422-441 (2023). Reviewer: Ranjeet Sehmi (Chandigarh) MSC: 11B65 11D61 × Cite Format Result Cite Review PDF 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 1524.11089 Int. J. Math. Comput. Sci. 18, No. 3, 525-527 (2023). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Viriyapong, Nongluk; Viriyapong, Chokchai On the Diophantine equation \(255^x+323^y=z^2\). (English) Zbl 1524.11090 Int. J. Math. Comput. Sci. 18, No. 3, 521-523 (2023). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: Link
Gayo, William S. jun.; Bacani, Jerico B. On the solutions of some Mersenne prime-involved Diophantine equations. (English) Zbl 1524.11080 Int. J. Math. Comput. Sci. 18, No. 3, 487-495 (2023). MSC: 11D61 × Cite Format Result Cite Review PDF 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 1524.11086 Int. J. Math. Comput. Sci. 18, No. 2, 205-209 (2023). MSC: 11D61 × Cite Format Result Cite Review PDF 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 1524.11087 Int. J. Math. Comput. Sci. 18, No. 2, 149-152 (2023). MSC: 11D61 × Cite Format Result Cite Review PDF 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 1524.11085 Int. J. Math. Comput. Sci. 18, No. 2, 143-147 (2023). MSC: 11D61 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF Full Text: DOI
Dimitrov, Stoyan A diophantine equation involving special prime numbers. (English) Zbl 1538.11172 Czech. Math. J. 73, No. 1, 151-176 (2023). MSC: 11P32 11L07 11L20 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF Full Text: DOI
Bennett, Michael A.; Siksek, Samir Differences between perfect powers: the Lebesgue-Nagell equation. (English) Zbl 1529.11056 Trans. Am. Math. Soc. 376, No. 1, 335-370 (2023). Reviewer: Gökhan Soydan (Bursa) MSC: 11D61 11D41 11F80 11F03 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
García, Pedro-José Cazorla On differences of perfect powers and prime powers. arXiv:2312.09985 Preprint, arXiv:2312.09985 [math.NT] (2023). MSC: 11D61 11D41 11D59 11F80 11F11 × Cite Format Result Cite Full Text: arXiv OA License
Pandichelvi, V.; Umamaheswari, B. Perceiving solutions for an exponential Diophantine equation linking safe and Sophie Germain primes \(q^x + p^y= z^2\). (English) Zbl 1538.11110 Jñānābha 52, No. 2, 165-167 (2022). MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: DOI
Hamtat, Abdelkader On the Diophantine equation on reciprocal Fibonacci numbers. (English) Zbl 1524.11082 Math. Appl. (Warsaw) 50, No. 2, 249-254 (2022). MSC: 11D61 11B39 × Cite Format Result Cite Review PDF Full Text: DOI
Luca, Florian Markov triples with two Fibonacci components. (English) Zbl 1530.11024 Rend. Semin. Mat. Univ. Padova 148, 213-243 (2022). Reviewer: Hayder Hashim (Kufa) MSC: 11B39 11D61 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF Full Text: DOI
Hoque, Azizul Generalized Mersenne numbers of the form \(cx^2\). (English) Zbl 1524.11012 Ann. Math. Inform. 55, 88-92 (2022). MSC: 11A51 11D61 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Alan, Murat Mersenne numbers as a difference of two Lucas numbers. (English) Zbl 1524.11030 Commentat. Math. Univ. Carol. 63, No. 3, 269-276 (2022). MSC: 11B39 11A51 11J86 11D61 × Cite Format Result Cite Review PDF Full Text: DOI
Luo, Raymond; Yu, Gang A ternary additive problem involving fractional powers. (English) Zbl 1531.11034 Involve 15, No. 4, 629-640 (2022). Reviewer: Guram Gogishvili (Tbilisi) MSC: 11D85 11L07 × Cite Format Result Cite Review PDF Full Text: DOI
Meher, N. K.; Rout, S. S. \(S\)-parts of sums of terms of linear recurrence sequences. (English) Zbl 1524.11024 Acta Math. Hung. 168, No. 2, 553-571 (2022). Reviewer: István Pink (Debrecen) MSC: 11B37 11D61 11J86 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF Full Text: DOI
Dima, Andreea A computer-based approach to solving the Diophantine equation \(7^x-3^y=100\). (English) Zbl 1520.11041 PUMP J. Undergrad. Res. 5, 161-164 (2022). MSC: 11D61 11Y50 × Cite Format Result Cite Review PDF 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 1518.11031 SUT J. Math. 58, No. 1, 77-89 (2022). Reviewer: Lajos Hajdu (Debrecen) MSC: 11D61 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF Full Text: DOI