Ghale, Vinodkumar; Das, Shamik; Chakraborty, Debopam A Heron triangle and a Diophantine equation. (English) Zbl 07692667 Period. Math. Hung. 86, No. 2, 503-537 (2023). MSC: 11G05 51M04 11D25 PDF BibTeX XML Cite \textit{V. Ghale} et al., Period. Math. Hung. 86, No. 2, 503--537 (2023; Zbl 07692667) Full Text: DOI
Hu, Yongzhong; Le, Maohua On the \(X\)-coordinates of Pell equations of the form \(px^2\). (English) Zbl 07672190 Period. Math. Hung. 86, No. 1, 281-288 (2023). MSC: 11B39 PDF BibTeX XML Cite \textit{Y. Hu} and \textit{M. Le}, Period. Math. Hung. 86, No. 1, 281--288 (2023; Zbl 07672190) Full Text: DOI
Konyagin, Sergei V.; Shparlinski, Igor E.; Vyugin, Ilya V. Polynomial equations in subgroups and applications. (English) Zbl 1509.11021 Avila, Artur (ed.) et al., Analysis at large. Dedicated to the life and work of Jean Bourgain. Cham: Springer. 273-297 (2022). MSC: 11D25 11G25 11T06 PDF BibTeX XML Cite \textit{S. V. Konyagin} et al., in: Analysis at large. Dedicated to the life and work of Jean Bourgain. Cham: Springer. 273--297 (2022; Zbl 1509.11021) Full Text: DOI arXiv
Tho, Nguyen Xuan Fermat quartics with only trivial solutions in any odd degree number field. (English) Zbl 07644676 Period. Math. Hung. 85, No. 2, 427-434 (2022). Reviewer: István Gaál (Debrecen) MSC: 11D25 11D41 PDF BibTeX XML Cite \textit{N. X. Tho}, Period. Math. Hung. 85, No. 2, 427--434 (2022; Zbl 07644676) Full Text: DOI
Zhang, Yong; Tang, Qiongzhi; Zhang, Yuna On the Diophantine equations \(z^2=f(x)^2 \pm f(y)^2\) involving Laurent polynomials. II. (English) Zbl 1503.11076 Miskolc Math. Notes 23, No. 2, 1023-1036 (2022). MSC: 11D72 11D25 11D41 11G05 PDF BibTeX XML Cite \textit{Y. Zhang} et al., Miskolc Math. Notes 23, No. 2, 1023--1036 (2022; Zbl 1503.11076) Full Text: DOI
Vaishya, Lalit; Sharma, Richa A class of fruit Diophantine equations. (English) Zbl 07605285 Monatsh. Math. 199, No. 4, 899-907 (2022). MSC: 11D25 14H52 PDF BibTeX XML Cite \textit{L. Vaishya} and \textit{R. Sharma}, Monatsh. Math. 199, No. 4, 899--907 (2022; Zbl 07605285) Full Text: DOI
Choudhry, Ajai Matrix morphology and composition of higher degree forms with applications to Diophantine equations. (English) Zbl 1497.11096 Rad Hrvat. Akad. Znan. Umjet., Mat. Znan. 551(26), 65-89 (2022). MSC: 11E76 11E16 11C20 11D25 11D41 PDF BibTeX XML Cite \textit{A. Choudhry}, Rad Hrvat. Akad. Znan. Umjet., Mat. Znan. 551(26), 65--89 (2022; Zbl 1497.11096) Full Text: DOI arXiv
Hashim, Hayder R.; Szalay, László; Tengely, Szabolcs Markoff-Rosenberger triples and generalized Lucas sequences. (English) Zbl 1513.11098 Period. Math. Hung. 85, No. 1, 188-202 (2022). Reviewer: Ivan Marin (Lyon) MSC: 11D25 11B39 11B83 PDF BibTeX XML Cite \textit{H. R. Hashim} et al., Period. Math. Hung. 85, No. 1, 188--202 (2022; Zbl 1513.11098) Full Text: DOI arXiv
Tho, N. X. The equation \(x^4+2^ny^4=z^4\) in algebraic number fields. (English) Zbl 1513.11099 Acta Math. Hung. 167, No. 1, 309-331 (2022). Reviewer: István Gaál (Debrecen) MSC: 11D25 11R16 PDF BibTeX XML Cite \textit{N. X. Tho}, Acta Math. Hung. 167, No. 1, 309--331 (2022; Zbl 1513.11099) Full Text: DOI
Hilgart, Tobias; Vukusic, Ingrid; Ziegler, Volker On a family of cubic Thue equations involving Fibonacci and Lucas numbers. (English) Zbl 1501.11049 Integers 22, Paper A31, 20 p. (2022). Reviewer: István Gaál (Debrecen) MSC: 11D59 11D25 11B39 PDF BibTeX XML Cite \textit{T. Hilgart} et al., Integers 22, Paper A31, 20 p. (2022; Zbl 1501.11049) Full Text: arXiv 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
Cotti, Giordano; Varchenko, Alexander The \(\ast \)-Markov equation for Laurent polynomials. (English) Zbl 1500.11027 Mosc. Math. J. 22, No. 1, 1-68 (2022). Reviewer: Hayder Hashim (Kufa) MSC: 11D25 14F08 34M40 PDF BibTeX XML Cite \textit{G. Cotti} and \textit{A. Varchenko}, Mosc. Math. J. 22, No. 1, 1--68 (2022; Zbl 1500.11027) Full Text: arXiv Link
Choudhry, Ajai; Bluskov, Iliya; James, Alexander A Diophantine equation inspired by Brahmagupta’s identity. (English) Zbl 1496.11052 Int. J. Number Theory 18, No. 4, 905-911 (2022). Reviewer: Arman Shamsi Zargar (Ardabil) MSC: 11D25 11D41 PDF BibTeX XML Cite \textit{A. Choudhry} et al., Int. J. Number Theory 18, No. 4, 905--911 (2022; Zbl 1496.11052) Full Text: DOI arXiv
Bhargava, Manjul On the number of monogenizations of a quartic order (with an appendix by Shabnam Akhtari). (English) Zbl 1499.11328 Publ. Math. Debr. 100, No. 3-4, 513-531 (2022). Reviewer: István Gaál (Debrecen) MSC: 11R16 11D09 PDF BibTeX XML Cite \textit{M. Bhargava}, Publ. Math. Debr. 100, No. 3--4, 513--531 (2022; Zbl 1499.11328) Full Text: DOI
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
Hirakawa, Yoshinosuke; Shimizu, Yosuke Counterexamples to the local-global principle for non-singular plane curves and a cubic analogue of Ankeny-Artin-Chowla-Mordell conjecture. (English) Zbl 1490.11039 Proc. Am. Math. Soc. 150, No. 5, 1821-1835 (2022). Reviewer: B. Z. Moroz (Bonn) MSC: 11D41 11D57 11E76 11N32 11R16 PDF BibTeX XML Cite \textit{Y. Hirakawa} and \textit{Y. Shimizu}, Proc. Am. Math. Soc. 150, No. 5, 1821--1835 (2022; Zbl 1490.11039) Full Text: DOI arXiv
Klaška, Jiří Quartic polynomials with a given discriminant. (English) Zbl 1486.11047 Math. Slovaca 72, No. 1, 35-50 (2022). Reviewer: István Gaál (Debrecen) MSC: 11D25 11D45 11Y50 PDF BibTeX XML Cite \textit{J. Klaška}, Math. Slovaca 72, No. 1, 35--50 (2022; Zbl 1486.11047) Full Text: DOI
Ahmadi, Mahnaz; Janfada, Ali S. On quartic Diophantine equations with trivial solutions in the Gaussian integer. (English) Zbl 1486.11046 Int. Electron. J. Algebra 31, 134-142 (2022). Reviewer: István Gaál (Debrecen) MSC: 11D25 11G05 11D45 PDF BibTeX XML Cite \textit{M. Ahmadi} and \textit{A. S. Janfada}, Int. Electron. J. Algebra 31, 134--142 (2022; Zbl 1486.11046) Full Text: DOI
Togbé, A.; Walsh, P. G. A classical approach to a parametric family of simultaneous Pell equations with applications to a family of Thue equations. (English) Zbl 1486.11048 Bol. Soc. Mat. Mex., III. Ser. 28, No. 1, Paper No. 4, 7 p. (2022). Reviewer: Maciej Ulas (Kraków) MSC: 11D25 11D59 PDF BibTeX XML Cite \textit{A. Togbé} and \textit{P. G. Walsh}, Bol. Soc. Mat. Mex., III. Ser. 28, No. 1, Paper No. 4, 7 p. (2022; Zbl 1486.11048) Full Text: DOI
Klaška, Jiří On cubic polynomials with a given discriminant. (English) Zbl 07614899 Math. Appl., Brno 10, No. 2, 103-113 (2021). MSC: 11D25 11D45 11Y50 PDF BibTeX XML Cite \textit{J. Klaška}, Math. Appl., Brno 10, No. 2, 103--113 (2021; Zbl 07614899) 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
Kumar, Wadhawan Narinder; Priyanka, Wadhawan A simple solution to Diophantine equations-fourth power. (English) Zbl 1499.11166 South East Asian J. Math. Math. Sci. 17, No. 1, 95-114 (2021). MSC: 11D25 PDF BibTeX XML Cite \textit{W. N. Kumar} and \textit{W. Priyanka}, South East Asian J. Math. Math. Sci. 17, No. 1, 95--114 (2021; Zbl 1499.11166) Full Text: Link
Kagawa, Takaaki The Diophantine equation \(X^3=u+v\) over real quadratic fields. II. (English) Zbl 1501.11046 Tokyo J. Math. 44, No. 2, 507-513 (2021). Reviewer: István Gaál (Debrecen) MSC: 11D25 PDF BibTeX XML Cite \textit{T. Kagawa}, Tokyo J. Math. 44, No. 2, 507--513 (2021; Zbl 1501.11046) Full Text: DOI
Guan, Xungui On the Diophantine equation \(x^3\pm 1=7qy^2\). (Chinese. English summary) Zbl 1488.11082 J. Cent. China Norm. Univ., Nat. Sci. 55, No. 4, 527-537 (2021). MSC: 11D25 PDF BibTeX XML Cite \textit{X. Guan}, J. Cent. China Norm. Univ., Nat. Sci. 55, No. 4, 527--537 (2021; Zbl 1488.11082) Full Text: DOI
Zhang, Yong; Gao, Dan On certain Diophantine equations concerning the area of right triangles. (English) Zbl 1478.51009 Math. Slovaca 71, No. 1, 171-182 (2021). MSC: 51M25 11D25 11D72 PDF BibTeX XML Cite \textit{Y. Zhang} and \textit{D. Gao}, Math. Slovaca 71, No. 1, 171--182 (2021; Zbl 1478.51009) Full Text: DOI
Hirakawa, Yoshinosuke; Kanamura, Yoshinori How to calculate the proportion of everywhere locally soluble diagonal hypersurfaces. (English) Zbl 1492.14038 Int. J. Number Theory 17, No. 10, 2361-2377 (2021). Reviewer: Arman Shamsi Zargar (Ardabil) MSC: 14G12 14G05 11D09 11D25 11D41 11D72 11E76 PDF BibTeX XML Cite \textit{Y. Hirakawa} and \textit{Y. Kanamura}, Int. J. Number Theory 17, No. 10, 2361--2377 (2021; Zbl 1492.14038) Full Text: DOI arXiv
Choudhry, Ajai New solutions of the Tarry-Escott problem of degrees 2, 3 and 5. (English) Zbl 1479.11057 J. Integer Seq. 24, No. 8, Article 21.8.1, 9 p. (2021). MSC: 11D72 11D25 11D41 PDF BibTeX XML Cite \textit{A. Choudhry}, J. Integer Seq. 24, No. 8, Article 21.8.1, 9 p. (2021; Zbl 1479.11057) Full Text: arXiv Link
Lin, Lijuan On the Diophantine equation \(7x(x + 1)(x + 2)(x + 3) = 5y(y + 1)(y + 2)(y + 3)\). (Chinese. English summary) Zbl 1488.11083 Math. Pract. Theory 51, No. 9, 218-223 (2021). MSC: 11D25 PDF BibTeX XML Cite \textit{L. Lin}, Math. Pract. Theory 51, No. 9, 218--223 (2021; Zbl 1488.11083)
Du, Xiaoying The number of positive integer points on the elliptic curve \({y^2} = pqx({x^2} + 2)\). (Chinese. English summary) Zbl 1488.14009 Math. Pract. Theory 51, No. 9, 205-209 (2021). MSC: 14H52 11D25 PDF BibTeX XML Cite \textit{X. Du}, Math. Pract. Theory 51, No. 9, 205--209 (2021; Zbl 1488.14009)
Zhang, Y. On products of consecutive arithmetic progressions. III. (English) Zbl 1480.11035 Acta Math. Hung. 163, No. 2, 407-428 (2021). Reviewer: Maciej Ulas (Kraków) MSC: 11D25 11D72 PDF BibTeX XML Cite \textit{Y. Zhang}, Acta Math. Hung. 163, No. 2, 407--428 (2021; Zbl 1480.11035) Full Text: DOI
Babić, S. Bujačić; Nabardi, K. On some Diophantine equations. (English) Zbl 1474.11091 Miskolc Math. Notes 22, No. 1, 65-75 (2021). MSC: 11D45 11D25 PDF BibTeX XML Cite \textit{S. B. Babić} and \textit{K. Nabardi}, Miskolc Math. Notes 22, No. 1, 65--75 (2021; Zbl 1474.11091) Full Text: DOI
Osipov, N. N.; Kytmanov, A. A. An algorithm for solving a family of fourth-degree Diophantine equations that satisfy Runge’s condition. (English. Russian original) Zbl 1476.11149 Program. Comput. Softw. 47, No. 1, 29-33 (2021); translation from Programmirovanie 47, No. 1, 39-44 (2021). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11Y50 11D25 PDF BibTeX XML Cite \textit{N. N. Osipov} and \textit{A. A. Kytmanov}, Program. Comput. Softw. 47, No. 1, 29--33 (2021; Zbl 1476.11149); translation from Programmirovanie 47, No. 1, 39--44 (2021) Full Text: DOI
Choudhry, Ajai Four biquadrates whose sum is a perfect square. (English) Zbl 1483.11060 J. Integer Seq. 24, No. 1, Article 21.1.8, 7 p. (2021). MSC: 11D25 PDF BibTeX XML Cite \textit{A. Choudhry}, J. Integer Seq. 24, No. 1, Article 21.1.8, 7 p. (2021; Zbl 1483.11060) Full Text: Link
Hashim, Hayder Raheem; Tengely, Szabolcs Solutions of a generalized Markoff equation in Fibonacci numbers. (English) Zbl 1482.11044 Math. Slovaca 70, No. 5, 1069-1078 (2020). MSC: 11D25 11B39 PDF BibTeX XML Cite \textit{H. R. Hashim} and \textit{S. Tengely}, Math. Slovaca 70, No. 5, 1069--1078 (2020; Zbl 1482.11044) Full Text: DOI Link
Guan, Xungui On the Diophantine equation \(y (y + 1) (y + 2) (y + 3) = 4{n^2}x (x + 1) (x + 2) (x + 3)\). (Chinese. English summary) Zbl 1474.11086 Math. Pract. Theory 50, No. 18, 243-247 (2020). MSC: 11D25 PDF BibTeX XML Cite \textit{X. Guan}, Math. Pract. Theory 50, No. 18, 243--247 (2020; Zbl 1474.11086)
Cereceda, José Luis Binary quadratic forms and sums of powers of integers. (English) Zbl 1474.11085 Ann. Math. Inform. 52, 71-84 (2020). MSC: 11D25 11B57 PDF BibTeX XML Cite \textit{J. L. Cereceda}, Ann. Math. Inform. 52, 71--84 (2020; Zbl 1474.11085) Full Text: DOI arXiv
Galyautdinov, I. G.; Lavrentyeva, E. E. Diophantine equation generated by the maximal subfield of a circular field. (English. Russian original) Zbl 1456.11203 Russ. Math. 64, No. 7, 38-47 (2020); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2020, No. 7, 45-55 (2020). MSC: 11R04 11R16 11D25 PDF BibTeX XML Cite \textit{I. G. Galyautdinov} and \textit{E. E. Lavrentyeva}, Russ. Math. 64, No. 7, 38--47 (2020; Zbl 1456.11203); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2020, No. 7, 45--55 (2020) Full Text: DOI
Zhang, Yong; Shen, Zhongyan Arithmetic properties of polynomials. (English) Zbl 1474.11088 Period. Math. Hung. 81, No. 1, 134-148 (2020). MSC: 11D25 11D72 11G05 PDF BibTeX XML Cite \textit{Y. Zhang} and \textit{Z. Shen}, Period. Math. Hung. 81, No. 1, 134--148 (2020; Zbl 1474.11088) Full Text: DOI arXiv
Zheng, Hui; Yang, Shichun The solutions of the equation of preimage distribution for a class of perfect nonlinear functions. (Chinese. English summary) Zbl 1488.94102 Math. Pract. Theory 50, No. 4, 263-268 (2020). MSC: 94B05 11T71 11D25 PDF BibTeX XML Cite \textit{H. Zheng} and \textit{S. Yang}, Math. Pract. Theory 50, No. 4, 263--268 (2020; Zbl 1488.94102)
Guan, Xungui On the Diophantine equation \(x^2-2y^4=M (M=17, 41, 73, 89, 97)\). (Chinese. English summary) Zbl 1463.11103 J. Cent. China Norm. Univ., Nat. Sci. 54, No. 2, 200-206 (2020). MSC: 11D25 PDF BibTeX XML Cite \textit{X. Guan}, J. Cent. China Norm. Univ., Nat. Sci. 54, No. 2, 200--206 (2020; Zbl 1463.11103) Full Text: DOI
Zhang, Yong; Shamsi Zargar, Arman On the Diophantine equations \(z^2=f(x)^2 \pm f(y)^2\) involving Laurent polynomials. (English) Zbl 1450.11029 Funct. Approximatio, Comment. Math. 62, No. 2, 187-201 (2020). Reviewer: Maciej Ulas (Kraków) MSC: 11D72 11D25 11D41 11G05 PDF BibTeX XML Cite \textit{Y. Zhang} and \textit{A. Shamsi Zargar}, Funct. Approximatio, Comment. Math. 62, No. 2, 187--201 (2020; Zbl 1450.11029) Full Text: DOI arXiv Euclid
Tengelys, Szabolcs Markoff-Rosenberger triples with Fibonacci components. (English) Zbl 1456.11033 Glas. Mat., III. Ser. 55, No. 1, 29-36 (2020). Reviewer: Anitha Srinivasan (Madrid) MSC: 11D45 11D25 11B39 PDF BibTeX XML Cite \textit{S. Tengelys}, Glas. Mat., III. Ser. 55, No. 1, 29--36 (2020; Zbl 1456.11033) Full Text: DOI Link
Cerbu, Alois; Gunther, Elijah; Magee, Michael; Peilen, Luke The cycle structure of a Markoff automorphism over finite fields. (English) Zbl 1459.37096 J. Number Theory 211, 1-27 (2020). MSC: 37P05 37P35 11D25 11G35 11F06 20B27 11G20 PDF BibTeX XML Cite \textit{A. Cerbu} et al., J. Number Theory 211, 1--27 (2020; Zbl 1459.37096) Full Text: DOI arXiv Link
Zhang, Yong; Chen, Deyi A Diophantine equation with the harmonic mean. (English) Zbl 1449.11070 Period. Math. Hung. 46, No. 1, 138-144 (2020). Reviewer: Thomas A. Schmidt (Corvallis) MSC: 11D72 11D25 11D41 11G05 PDF BibTeX XML Cite \textit{Y. Zhang} and \textit{D. Chen}, Period. Math. Hung. 46, No. 1, 138--144 (2020; Zbl 1449.11070) Full Text: DOI
Gallegos-Ruiz, H. R.; Katsipis, N.; Tengely, Sz.; Ulas, M. On the Diophantine equation \(\binom{n}{k} = \binom{m}{l} + d\). (English) Zbl 1451.11020 J. Number Theory 208, 418-440 (2020). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11D25 11D41 11G30 11G05 11J86 PDF BibTeX XML Cite \textit{H. R. Gallegos-Ruiz} et al., J. Number Theory 208, 418--440 (2020; Zbl 1451.11020) Full Text: DOI arXiv
Gaál, István Calculating relative power integral bases in totally complex quartic extensions of totally real fields. (English) Zbl 1490.11121 JP J. Algebra Number Theory Appl. 44, No. 2, 129-157 (2019). MSC: 11Y50 11R04 11D57 11D59 PDF BibTeX XML Cite \textit{I. Gaál}, JP J. Algebra Number Theory Appl. 44, No. 2, 129--157 (2019; Zbl 1490.11121) Full Text: DOI arXiv
Osipov, Nikolai N.; Medvedeva, Maria I. An elementary algorithm for solving a Diophantine equation of degree four with Runge’s condition. (English) Zbl 1465.11235 J. Sib. Fed. Univ., Math. Phys. 12, No. 3, 331-341 (2019). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11Y16 11D25 PDF BibTeX XML Cite \textit{N. N. Osipov} and \textit{M. I. Medvedeva}, J. Sib. Fed. Univ., Math. Phys. 12, No. 3, 331--341 (2019; Zbl 1465.11235) Full Text: DOI MNR
Janfada, Ali S.; Nabardi, Kamran On Diophantine equation \(x^4+y^4=n(u^4+v^4)\). (English) Zbl 1485.11071 Math. Slovaca 69, No. 6, 1245-1248 (2019). MSC: 11D25 PDF BibTeX XML Cite \textit{A. S. Janfada} and \textit{K. Nabardi}, Math. Slovaca 69, No. 6, 1245--1248 (2019; Zbl 1485.11071) Full Text: DOI
Kureš, Miroslav Number theoretical views on resonant Rossby wave triads: graphs with vertices on quartics. (English) Zbl 1440.76013 Nonlinear Phenom. Complex Syst., Minsk 22, No. 3, 285-291 (2019). MSC: 76B15 11Z05 11D25 PDF BibTeX XML Cite \textit{M. Kureš}, Nonlinear Phenom. Complex Syst., Minsk 22, No. 3, 285--291 (2019; Zbl 1440.76013)
Guan, Xungui On the Diophantine equation \(X^2 + 4Y^4 = pZ^4\). (Chinese. English summary) Zbl 1449.11057 Math. Pract. Theory 49, No. 18, 279-284 (2019). MSC: 11D25 PDF BibTeX XML Cite \textit{X. Guan}, Math. Pract. Theory 49, No. 18, 279--284 (2019; Zbl 1449.11057)
Li, Jianglong; Luo, Ming; Lin, Lijuan On the positive integer solution of Diophantine equation \(x (x+1) (x+2) (x+3) = 42y (y+1) (y+2) (y+3)\). (Chinese. English summary) Zbl 1449.11058 Basic Sci. J. Text. Univ. 32, No. 3, 293-297 (2019). MSC: 11D25 PDF BibTeX XML Cite \textit{J. Li} et al., Basic Sci. J. Text. Univ. 32, No. 3, 293--297 (2019; Zbl 1449.11058) Full Text: DOI
Guan, Xungui Integral points on the elliptic curve \(y^2 = x^3 + (m - 4)x - 2m\). (Chinese. English summary) Zbl 1449.11056 Adv. Math., Beijing 48, No. 6, 721-730 (2019). MSC: 11D25 11G05 PDF BibTeX XML Cite \textit{X. Guan}, Adv. Math., Beijing 48, No. 6, 721--730 (2019; Zbl 1449.11056)
Reznick, Bruce Linearly dependent powers of binary quadratic forms. (English) Zbl 1456.11044 Pac. J. Math. 303, No. 2, 729-755 (2019). MSC: 11E76 11P05 14M99 11D25 11D41 PDF BibTeX XML Cite \textit{B. Reznick}, Pac. J. Math. 303, No. 2, 729--755 (2019; Zbl 1456.11044) Full Text: DOI arXiv
Deng, Mou-Jie; Guo, Jin Application of quartic residue character theory to the Diophantine equation \(a^x+b^y=c^z\). (English) Zbl 1449.11064 Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 62(110), No. 2, 133-139 (2019). Reviewer: István Gaál (Debrecen) MSC: 11D61 PDF BibTeX XML Cite \textit{M.-J. Deng} and \textit{J. Guo}, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 62(110), No. 2, 133--139 (2019; Zbl 1449.11064)
Granville, Andrew Number theory revealed: a masterclass. (English) Zbl 1454.11002 Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4158-6/hbk; 978-1-4704-5424-1/ebook). xxviii, 587 p. (2019). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-01 11A55 11B30 11B39 11D09 11D25 11N05 11N25 PDF BibTeX XML Cite \textit{A. Granville}, Number theory revealed: a masterclass. Providence, RI: American Mathematical Society (AMS) (2019; Zbl 1454.11002)
Park, Jinseo; Lee, June Bok Some family of Diophantine pairs with Fibonacci numbers. (English) Zbl 1456.11032 Indian J. Pure Appl. Math. 50, No. 2, 367-384 (2019). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D09 11D25 11B39 PDF BibTeX XML Cite \textit{J. Park} and \textit{J. B. Lee}, Indian J. Pure Appl. Math. 50, No. 2, 367--384 (2019; Zbl 1456.11032) Full Text: DOI
Gamburd, Alexander; Magee, Michael; Ronan, Ryan An asymptotic formula for integer points on Markoff-Hurwitz varieties. (English) Zbl 1447.11051 Ann. Math. (2) 190, No. 3, 751-809 (2019). Reviewer: Arthur Baragar (Las Vegas) MSC: 11D45 11D25 11D41 11J70 37D25 37D35 PDF BibTeX XML Cite \textit{A. Gamburd} et al., Ann. Math. (2) 190, No. 3, 751--809 (2019; Zbl 1447.11051) Full Text: DOI arXiv Link
Zhang, Yong; Shamsi Zargar, Arman On the Diophantine equation \(f(x)f(y)=f(z)^n\) involving Laurent polynomials. II. (English) Zbl 1450.11028 Colloq. Math. 158, No. 1, 119-126 (2019). Reviewer: Maciej Ulas (Kraków) MSC: 11D72 11D25 11D41 11G05 PDF BibTeX XML Cite \textit{Y. Zhang} and \textit{A. Shamsi Zargar}, Colloq. Math. 158, No. 1, 119--126 (2019; Zbl 1450.11028) Full Text: DOI
Choudhry, Ajai Symmetric Diophantine systems and families of elliptic curves of high rank. (English) Zbl 1457.11074 Rocky Mt. J. Math. 49, No. 5, 1419-1447 (2019). Reviewer: Maciej Ulas (Kraków) MSC: 11G05 11D25 11D41 PDF BibTeX XML Cite \textit{A. Choudhry}, Rocky Mt. J. Math. 49, No. 5, 1419--1447 (2019; Zbl 1457.11074) Full Text: DOI arXiv Euclid
Zhang, Yong; Shamsi Zargar, Arman On the Diophantine equations \(z^2=f(x)^2\pm f(y)^2\) involving quartic polynomials. (English) Zbl 1438.11090 Period. Math. Hung. 79, No. 1, 25-31 (2019). Reviewer: Thomas Schmidt (Corvallis) MSC: 11D72 11D25 11D41 11G05 PDF BibTeX XML Cite \textit{Y. Zhang} and \textit{A. Shamsi Zargar}, Period. Math. Hung. 79, No. 1, 25--31 (2019; Zbl 1438.11090) Full Text: DOI
Yang, Hai; Fu, Ruiqin Integral points on the elliptic curve \(y^2=x^3-4p^2x\). (English) Zbl 1513.11137 Czech. Math. J. 69, No. 3, 853-862 (2019). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G05 11D25 11Y50 PDF BibTeX XML Cite \textit{H. Yang} and \textit{R. Fu}, Czech. Math. J. 69, No. 3, 853--862 (2019; Zbl 1513.11137) Full Text: DOI
Leung, Ho-Hon On Diophantine equations of Nathanson. (English) Zbl 1446.11053 Palest. J. Math. 8, No. 2, 40-44 (2019). Reviewer: István Gaál (Debrecen) MSC: 11D41 11D25 PDF BibTeX XML Cite \textit{H.-H. Leung}, Palest. J. Math. 8, No. 2, 40--44 (2019; Zbl 1446.11053) Full Text: Link
Hajja, Mowaffaq; Sondow, Jonathan Newton quadrilaterals, the associated cubic equations, and their rational solutions. (English) Zbl 1472.11094 Am. Math. Mon. 126, No. 2, 135-150 (2019). MSC: 11D25 PDF BibTeX XML Cite \textit{M. Hajja} and \textit{J. Sondow}, Am. Math. Mon. 126, No. 2, 135--150 (2019; Zbl 1472.11094) Full Text: DOI
Liu, Jie On the Diophantine equation \(x(x + 1)(x + 2)(x + 3) = 15y(y + 1)(y + 2)(y + 3)\). (Chinese. English summary) Zbl 1424.11077 J. Yunnan Minzu Univ., Nat. Sci. 27, No. 5, 403-407 (2018). MSC: 11D25 PDF BibTeX XML Cite \textit{J. Liu}, J. Yunnan Minzu Univ., Nat. Sci. 27, No. 5, 403--407 (2018; Zbl 1424.11077) Full Text: DOI
Zhang, Y. On products of consecutive arithmetic progressions. II. (English) Zbl 1424.11078 Acta Math. Hung. 156, No. 1, 240-254 (2018). Reviewer: Thomas Schmidt (Corvallis) MSC: 11D25 11D72 PDF BibTeX XML Cite \textit{Y. Zhang}, Acta Math. Hung. 156, No. 1, 240--254 (2018; Zbl 1424.11078) Full Text: DOI
Jena, Susil Kumar On \(x^n + y^n = n! z^n\). (English) Zbl 1440.11034 Commun. Math. 26, No. 1, 11-14 (2018). MSC: 11D25 11D41 PDF BibTeX XML Cite \textit{S. K. Jena}, Commun. Math. 26, No. 1, 11--14 (2018; Zbl 1440.11034) Full Text: Link
Luca, Florian; Srinivasan, Anitha Markov equation with Fibonacci components. (English) Zbl 1458.11056 Fibonacci Q. 56, No. 2, 126-129 (2018). MSC: 11D45 11B39 11D25 PDF BibTeX XML Cite \textit{F. Luca} and \textit{A. Srinivasan}, Fibonacci Q. 56, No. 2, 126--129 (2018; Zbl 1458.11056) Full Text: Link
Meiri, Chen; Puder, Doron [Carmon, Dan] The Markoff group of transformations in prime and composite moduli. With an appendix by Dan Carmon. (English) Zbl 1447.11049 Duke Math. J. 167, No. 14, 2679-2720 (2018). MSC: 11D25 20B15 20B25 20E05 PDF BibTeX XML Cite \textit{C. Meiri} and \textit{D. Puder}, Duke Math. J. 167, No. 14, 2679--2720 (2018; Zbl 1447.11049) Full Text: DOI arXiv Euclid
Guan, Xungui Integral points on the elliptic curve \(y^2 = x(x - p)( x - q)\). I. (Chinese. English summary) Zbl 1424.11075 Math. Pract. Theory 48, No. 4, 272-279 (2018). MSC: 11D25 11G05 PDF BibTeX XML Cite \textit{X. Guan}, Math. Pract. Theory 48, No. 4, 272--279 (2018; Zbl 1424.11075)
Li, Yulong; Wan, Fei On integer solution of the Diophantine equation \({x^3} - 1 = 3P{y^2}\). (Chinese. English summary) Zbl 1413.11065 J. Qufu Norm. Univ., Nat. Sci. 44, No. 1, 25-28, 35 (2018). MSC: 11D25 PDF BibTeX XML Cite \textit{Y. Li} and \textit{F. Wan}, J. Qufu Norm. Univ., Nat. Sci. 44, No. 1, 25--28, 35 (2018; Zbl 1413.11065)
Guan, Xungui Integral points on the elliptic curve \(y^2 = x(x - p)(x - q)\). II. (Chinese. English summary) Zbl 1424.11074 J. Anhui Univ., Nat. Sci. 42, No. 2, 41-46 (2018). MSC: 11D25 11G05 PDF BibTeX XML Cite \textit{X. Guan}, J. Anhui Univ., Nat. Sci. 42, No. 2, 41--46 (2018; Zbl 1424.11074) Full Text: DOI
Hu, Jiayuan; Li, Xiaoxue On the quartic Thue equation \(a{x^4} - (2a + 1){x^2}{y^2} + a{y^4} = - 1\). (Chinese. English summary) Zbl 1413.11063 Basic Sci. J. Text. Univ. 31, No. 1, 35-37, 54 (2018). MSC: 11D25 PDF BibTeX XML Cite \textit{J. Hu} and \textit{X. Li}, Basic Sci. J. Text. Univ. 31, No. 1, 35--37, 54 (2018; Zbl 1413.11063) Full Text: DOI
Yang, Xiaoliu; Mu, Quanwu On the Diophantine equation \({x^3} - 1 = 229{y^2}\). (Chinese. English summary) Zbl 1413.11066 Basic Sci. J. Text. Univ. 31, No. 1, 31-34 (2018). MSC: 11D25 PDF BibTeX XML Cite \textit{X. Yang} and \textit{Q. Mu}, Basic Sci. J. Text. Univ. 31, No. 1, 31--34 (2018; Zbl 1413.11066) Full Text: DOI
Huong, Phạm Lan On the Diophantine equation \(x^3 + y^3 + z^3 = q\). (English) Zbl 1447.11048 Int. J. Number Theory 14, No. 8, 2205-2217 (2018). MSC: 11D25 PDF BibTeX XML Cite \textit{P. L. Huong}, Int. J. Number Theory 14, No. 8, 2205--2217 (2018; Zbl 1447.11048) Full Text: DOI
Choudhry, Ajai A new method of solving certain quartic and higher degree Diophantine equations. (English) Zbl 1407.11046 Int. J. Number Theory 14, No. 8, 2129-2154 (2018). MSC: 11D25 11D41 14G05 PDF BibTeX XML Cite \textit{A. Choudhry}, Int. J. Number Theory 14, No. 8, 2129--2154 (2018; Zbl 1407.11046) Full Text: DOI arXiv
Schinzel, A. On the congruence \(f(x)+g(y)+c\equiv 0\pmod{xy}\). II: The quadratic case. (English) Zbl 1410.11004 Acta Arith. 184, No. 1, 1-6 (2018). MSC: 11A07 11D09 11D25 11D41 PDF BibTeX XML Cite \textit{A. Schinzel}, Acta Arith. 184, No. 1, 1--6 (2018; Zbl 1410.11004) Full Text: DOI
Kim, Dohyeong Descent for the punctured universal elliptic curve, and the average number of integral points on elliptic curves. (English) Zbl 1441.11145 Acta Arith. 183, No. 3, 201-222 (2018). Reviewer: José María Tornero (Sevilla) MSC: 11G05 11D25 11D59 PDF BibTeX XML Cite \textit{D. Kim}, Acta Arith. 183, No. 3, 201--222 (2018; Zbl 1441.11145) Full Text: DOI arXiv
Shabani-Solt, Hassan; Janfada, Ali S. A lower bound for the number of integral solutions of Mordell equation. (English) Zbl 1434.11079 Kodai Math. J. 41, No. 1, 160-166 (2018). MSC: 11D09 11D25 11D45 11G05 PDF BibTeX XML Cite \textit{H. Shabani-Solt} and \textit{A. S. Janfada}, Kodai Math. J. 41, No. 1, 160--166 (2018; Zbl 1434.11079) Full Text: DOI Euclid
Schinzel, A.; Skałba, M. On certain biquadratic equations. II. (English) Zbl 1441.11061 Int. J. Number Theory 14, No. 7, 2095-2105 (2018). Reviewer: István Gaál (Debrecen) MSC: 11D25 11D09 PDF BibTeX XML Cite \textit{A. Schinzel} and \textit{M. Skałba}, Int. J. Number Theory 14, No. 7, 2095--2105 (2018; Zbl 1441.11061) Full Text: DOI
Izadi, Farzali; Rasool, Naghdali Forooshani; Amaneh, Amiryousefi Varnousfaderani Fourth power Diophantine equations in Gaussian integers. (English) Zbl 1391.11066 Proc. Indian Acad. Sci., Math. Sci. 128, No. 2, Paper No. 18, 6 p. (2018). MSC: 11D45 11D25 11G05 PDF BibTeX XML Cite \textit{F. Izadi} et al., Proc. Indian Acad. Sci., Math. Sci. 128, No. 2, Paper No. 18, 6 p. (2018; Zbl 1391.11066) Full Text: DOI
Zhang, Yong On the Diophantine equation \(f(x)f(y)=f(z)^n\) involving Laurent polynomials. (English) Zbl 1431.11050 Colloq. Math. 151, No. 1, 111-122 (2018). Reviewer: Thomas Schmidt (Corvallis) MSC: 11D72 11D25 11D41 11G05 PDF BibTeX XML Cite \textit{Y. Zhang}, Colloq. Math. 151, No. 1, 111--122 (2018; Zbl 1431.11050) Full Text: DOI arXiv
Choudhry, Ajai; Wróblewski, Jarosław An ancient Diophantine equation with applications to numerical curios and geometric series. (English) Zbl 1402.11049 Colloq. Math. 151, No. 1, 1-7 (2018). MSC: 11D25 PDF BibTeX XML Cite \textit{A. Choudhry} and \textit{J. Wróblewski}, Colloq. Math. 151, No. 1, 1--7 (2018; Zbl 1402.11049) Full Text: DOI arXiv
Netay, Igor V.; Savvateev, Alexei V. Sharygin triangles and elliptic curves. (English) Zbl 1437.11047 Bull. Korean Math. Soc. 54, No. 5, 1597-1617 (2017). MSC: 11D25 14H52 51M04 97G40 PDF BibTeX XML Cite \textit{I. V. Netay} and \textit{A. V. Savvateev}, Bull. Korean Math. Soc. 54, No. 5, 1597--1617 (2017; Zbl 1437.11047) Full Text: DOI arXiv
Li, Zhigang; Chen, Shexi A note on a family of quartic Thue equations with three parameters. (Chinese. English summary) Zbl 1399.11092 J. Syst. Sci. Math. Sci. 37, No. 10, 2138-2145 (2017). MSC: 11D25 11D59 PDF BibTeX XML Cite \textit{Z. Li} and \textit{S. Chen}, J. Syst. Sci. Math. Sci. 37, No. 10, 2138--2145 (2017; Zbl 1399.11092)
Yang, Hai; Hou, Jing; Fu, Ruiqin On the solvability of the cubic Diophantine equation \({x^3}+1=2{p_1}{p_2}Q{y^2}\). (Chinese. English summary) Zbl 1399.11094 Acta Sci. Nat. Univ. Sunyatseni 56, No. 5, 30-33 (2017). MSC: 11D25 PDF BibTeX XML Cite \textit{H. Yang} et al., Acta Sci. Nat. Univ. Sunyatseni 56, No. 5, 30--33 (2017; Zbl 1399.11094) Full Text: DOI
Chen, Fengjuan Research on the properties of the Markoff numbers. (Chinese. English summary) Zbl 1399.11090 Acta Math. Sin., Chin. Ser. 60, No. 6, 977-982 (2017). MSC: 11D25 PDF BibTeX XML Cite \textit{F. Chen}, Acta Math. Sin., Chin. Ser. 60, No. 6, 977--982 (2017; Zbl 1399.11090)
Pan, Xiaowei A note on the arithmetic functional equation \(\sigma \left ( {{x^3}} \right) = {y^2}\). (Chinese. English summary) Zbl 1399.11093 Basic Sci. J. Text. Univ. 30, No. 3, 302-304, 310 (2017). MSC: 11D25 PDF BibTeX XML Cite \textit{X. Pan}, Basic Sci. J. Text. Univ. 30, No. 3, 302--304, 310 (2017; Zbl 1399.11093) Full Text: DOI
Choudhry, Ajai A note on the quartic Diophantine equation \(A^4+hB^4= C^4+hD^4\). (English) Zbl 1386.11057 Notes Number Theory Discrete Math. 23, No. 1, 1-3 (2017). MSC: 11D25 PDF BibTeX XML Cite \textit{A. Choudhry}, Notes Number Theory Discrete Math. 23, No. 1, 1--3 (2017; Zbl 1386.11057) Full Text: arXiv Link
Hamtat, Abdelkader; Behloul, Djilali On a Diophantine equation on triangular numbers. (English) Zbl 1399.11091 Miskolc Math. Notes 18, No. 2, 779-786 (2017). MSC: 11D25 11D41 PDF BibTeX XML Cite \textit{A. Hamtat} and \textit{D. Behloul}, Miskolc Math. Notes 18, No. 2, 779--786 (2017; Zbl 1399.11091) Full Text: DOI
Deng, Mou-Jie; Guo, Jin A note on Jeśmanowicz’ conjecture concerning primitive Pythagorean triples. II. (English) Zbl 1399.11099 Acta Math. Hung. 153, No. 2, 436-448 (2017). Reviewer: Jan-Hendrik Evertse (Leiden) MSC: 11D61 PDF BibTeX XML Cite \textit{M.-J. Deng} and \textit{J. Guo}, Acta Math. Hung. 153, No. 2, 436--448 (2017; Zbl 1399.11099) Full Text: DOI
Javanpeykar, Ariyan Effectively computing integral points on the moduli of smooth quartic curves. (English) Zbl 1395.14007 Q. J. Math. 68, No. 2, 345-358 (2017). Reviewer: Elisa Lorenzo García (Rennes) MSC: 14D23 11D45 11G50 11R27 14H10 14H50 PDF BibTeX XML Cite \textit{A. Javanpeykar}, Q. J. Math. 68, No. 2, 345--358 (2017; Zbl 1395.14007) Full Text: DOI arXiv
He, Zongyou On the Diophantine equation \(y(y + 1)(y + 2)(y + 3) = n^2x(x + 1)(x + 2)(x + 3)\). (Chinese. English summary) Zbl 1389.11080 J. Yunnan Minzu Univ., Nat. Sci. 26, No. 2, 137-139, 143 (2017). MSC: 11D25 PDF BibTeX XML Cite \textit{Z. He}, J. Yunnan Minzu Univ., Nat. Sci. 26, No. 2, 137--139, 143 (2017; Zbl 1389.11080)
Fan, Miao On the Diophantine equation \(x^3-1 = 181y^2\). (Chinese. English summary) Zbl 1374.11048 J. Yunnan Minzu Univ., Nat. Sci. 26, No. 1, 38-40 (2017). MSC: 11D25 PDF BibTeX XML Cite \textit{M. Fan}, J. Yunnan Minzu Univ., Nat. Sci. 26, No. 1, 38--40 (2017; Zbl 1374.11048)
Bremner, Andrew; Ulas, Maciej On representing coordinates of points on elliptic curves by quadratic forms. (English) Zbl 1435.11064 Acta Arith. 179, No. 1, 55-78 (2017). Reviewer: Bartosz Naskrecki (Poznań) MSC: 11D25 11D41 11E16 11G05 PDF BibTeX XML Cite \textit{A. Bremner} and \textit{M. Ulas}, Acta Arith. 179, No. 1, 55--78 (2017; Zbl 1435.11064) Full Text: DOI arXiv
Kishimoto, Nobu; Yoneda, Tsuyoshi A number theoretical observation of a resonant interaction of Rossby waves. (English) Zbl 1428.11058 Kodai Math. J. 40, No. 1, 16-20 (2017). MSC: 11D25 85A20 86A10 PDF BibTeX XML Cite \textit{N. Kishimoto} and \textit{T. Yoneda}, Kodai Math. J. 40, No. 1, 16--20 (2017; Zbl 1428.11058) Full Text: DOI arXiv Euclid
Nathanson, Melvyn B. On a Diophantine equation of M. J. Karama. (English) Zbl 1364.11080 Palest. J. Math. 6, No. 2, 524-526 (2017). MSC: 11D25 11D41 11A99 PDF BibTeX XML Cite \textit{M. B. Nathanson}, Palest. J. Math. 6, No. 2, 524--526 (2017; Zbl 1364.11080) Full Text: arXiv Link
Choudhry, Ajai; Wróblewski, Jarosław Triads of integers with equal sums of squares and equal products and a related multigrade chain. (English) Zbl 1428.11055 Acta Arith. 178, No. 1, 87-100 (2017). MSC: 11D09 11D25 11D41 PDF BibTeX XML Cite \textit{A. Choudhry} and \textit{J. Wróblewski}, Acta Arith. 178, No. 1, 87--100 (2017; Zbl 1428.11055) Full Text: DOI
Levesque, Claude; Waldschmidt, Michel Solving simultaneously Thue equations in the almost totally imaginary case. (English) Zbl 1418.11053 Murty, Vijaya Kumar (ed.) et al., Highly composite: papers in number theory. On the occasion of R. Balsubramanian’s 60th birth anniversary. Including papers from the international meeting on number theory, Harish-Chandra Research Institute, Allahabad, India, December 15–20, 2011. Mysore: Ramanujan Mathematical Society. Ramanujan Math. Soc. Lect. Notes Ser. 23, 137-156 (2016). MSC: 11D61 11D25 11D41 11D59 PDF BibTeX XML Cite \textit{C. Levesque} and \textit{M. Waldschmidt}, Ramanujan Math. Soc. Lect. Notes Ser. 23, 137--156 (2016; Zbl 1418.11053) Full Text: arXiv
Gao, Li; Zhao, Qifen Integral solutions of Diophantine equation \(x^3-1=55y^2\). (Chinese. English summary) Zbl 1374.11049 J. Yunnan Minzu Univ., Nat. Sci. 25, No. 6, 529-530 (2016). MSC: 11D25 PDF BibTeX XML Cite \textit{L. Gao} and \textit{Q. Zhao}, J. Yunnan Minzu Univ., Nat. Sci. 25, No. 6, 529--530 (2016; Zbl 1374.11049)
Abdelalim, Seddik; El Adlouni, Hassan; Diany, Hassan The Diophantine equation \(x^3+y^3=2z^2\). (English) Zbl 1380.11022 Gulf J. Math. 4, No. 4, 67-73 (2016). MSC: 11D25 11D09 PDF BibTeX XML Cite \textit{S. Abdelalim} et al., Gulf J. Math. 4, No. 4, 67--73 (2016; Zbl 1380.11022) Full Text: Link