Ziegler, Volker On a variant of Pillai’s problem involving \(S\)-units and Fibonacci numbers. (English) Zbl 07567635 Bol. Soc. Mat. Mex., III. Ser. 28, No. 3, Paper No. 57, 37 p. (2022). MSC: 11D61 11B39 11D45 11Y50 PDF BibTeX XML Cite \textit{V. Ziegler}, Bol. Soc. Mat. Mex., III. Ser. 28, No. 3, Paper No. 57, 37 p. (2022; Zbl 07567635) Full Text: DOI OpenURL
Ghadermarzi, Amir On the exceptional solutions of Jeśmanowicz’ conjecture. (English) Zbl 07551778 Bull. Iran. Math. Soc. 48, No. 3, 933-949 (2022). MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{A. Ghadermarzi}, Bull. Iran. Math. Soc. 48, No. 3, 933--949 (2022; Zbl 07551778) Full Text: DOI OpenURL
Fujita, Yasutsugu; Le, Maohua A note on the number of solutions of the Pillai type equation \(| a^x - b^y | = k\). (English) Zbl 07538056 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 07538056) Full Text: DOI OpenURL
Bajpai, Prajeet; Bennett, Michael A. A note on pencils of norm-form equations. (English) Zbl 07517642 Acta Arith. 203, No. 1, 19-26 (2022). 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 OpenURL
Vukusic, Ingrid; Ziegler, Volker Consecutive tuples of multiplicatively dependent integers. (English) Zbl 07493026 J. Number Theory 236, 280-307 (2022). MSC: 11N25 11D61 11J86 PDF BibTeX XML Cite \textit{I. Vukusic} and \textit{V. Ziegler}, J. Number Theory 236, 280--307 (2022; Zbl 07493026) Full Text: DOI arXiv OpenURL
Yang, Hai; Fu, Ruiqin A further note on Jeśmanowicz’ conjecture concerning primitive Pythagorean triples. (English) Zbl 07488613 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 07488613) Full Text: DOI OpenURL
Fujita, Yasutsugu; Le, Maohua Dem’janenko’s theorem on Jeśmanowicz’ conjecture concerning Pythagorean triples revisited. (English) Zbl 07419034 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 07419034) Full Text: DOI OpenURL
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 07410933 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 07410933) Full Text: DOI OpenURL
Rihane, Salah Eddine; Hernane, Mohand Ouamar; Togbé, Alain Solutions of a class of quartic Thue inequalities. (English) Zbl 07410372 Bol. Soc. Mat. Mex., III. Ser. 27, No. 2, Paper No. 57, 14 p. (2021). Reviewer: Günter Lettl (Graz) MSC: 11D59 11D09 11J86 PDF BibTeX XML Cite \textit{S. E. Rihane} et al., Bol. Soc. Mat. Mex., III. Ser. 27, No. 2, Paper No. 57, 14 p. (2021; Zbl 07410372) Full Text: DOI OpenURL
Bliznac Trebješanin, M. Extension of a Diophantine triple with the property \(D(4)\). (English) Zbl 07399062 Acta Math. Hung. 163, No. 1, 213-246 (2021). MSC: 11D09 11D45 11J86 PDF BibTeX XML Cite \textit{M. Bliznac Trebješanin}, Acta Math. Hung. 163, No. 1, 213--246 (2021; Zbl 07399062) Full Text: DOI arXiv OpenURL
Drungilas, Paulius; Garunkštis, Ramūnas; Novikas, Aivaras On second moment of Selberg zeta-function for \(\sigma =1\). (English) Zbl 1476.11118 Result. Math. 76, No. 4, Paper No. 184, 18 p. (2021). Reviewer: Shin-ya Koyama (Yokohama) MSC: 11M26 11M36 11M41 PDF BibTeX XML Cite \textit{P. Drungilas} et al., Result. Math. 76, No. 4, Paper No. 184, 18 p. (2021; Zbl 1476.11118) Full Text: DOI OpenURL
Fujita, Yasutsugu; Le, Maohua A note on Jeśmanowicz’ conjecture concerning nonprimitive Pythagorean triples. (English) Zbl 1471.11124 Bull. Aust. Math. Soc. 104, No. 1, 29-39 (2021). MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{Y. Fujita} and \textit{M. Le}, Bull. Aust. Math. Soc. 104, No. 1, 29--39 (2021; Zbl 1471.11124) Full Text: DOI OpenURL
Ji, Qingzhong; Qin, Hourong Exponential Diophantine equations \(p^m-p^n=q^s-q^t\). (English) Zbl 1468.11093 J. Ramanujan Math. Soc. 35, No. 3, 227-240 (2020). MSC: 11D61 11D72 PDF BibTeX XML Cite \textit{Q. Ji} and \textit{H. Qin}, J. Ramanujan Math. Soc. 35, No. 3, 227--240 (2020; Zbl 1468.11093) Full Text: Link OpenURL
Earp-Lynch, B.; Earp-Lynch, S.; Kihel, O. On certain \(D(9)\) and \(D(64)\) Diophantine triples. (English) Zbl 1474.11079 Acta Math. Hung. 162, No. 2, 483-517 (2020). Reviewer: Florian Luca (Johannesburg) MSC: 11D09 11D45 11B37 11J86 PDF BibTeX XML Cite \textit{B. Earp-Lynch} et al., Acta Math. Hung. 162, No. 2, 483--517 (2020; Zbl 1474.11079) Full Text: DOI OpenURL
Bai, Hairong; Kızıldere, Elif; Soydan, Gökhan; Yuan, Pingzhi On the exponential Diophantine equation \((n-1)^x+(n+2)^y=n^z\). (English) Zbl 1464.11036 Colloq. Math. 161, No. 2, 239-249 (2020). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{H. Bai} et al., Colloq. Math. 161, No. 2, 239--249 (2020; Zbl 1464.11036) Full Text: DOI arXiv OpenURL
Kizildere, Elif; Soydan, Gokhan On the Diophantine equation \((5pn^2 - 1)^x + (p(p - 5)n^2 + 1)^y=(pn)^z\). (English) Zbl 1478.11047 Honam Math. J. 42, No. 1, 139-150 (2020). MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{E. Kizildere} and \textit{G. Soydan}, Honam Math. J. 42, No. 1, 139--150 (2020; Zbl 1478.11047) Full Text: DOI arXiv OpenURL
Cipu, Mihai; Filipin, Alan; Fujita, Yasutsugu An infinite two-parameter family of Diophantine triples. (English) Zbl 1452.11031 Bull. Malays. Math. Sci. Soc. (2) 43, No. 1, 481-498 (2020). Reviewer: István Gaál (Debrecen) MSC: 11D09 11B37 11J86 PDF BibTeX XML Cite \textit{M. Cipu} et al., Bull. Malays. Math. Sci. Soc. (2) 43, No. 1, 481--498 (2020; Zbl 1452.11031) Full Text: DOI OpenURL
Cipu, Mihai; Filipin, Alan; Fujita, Yasutsugu Diophantine pairs that induce certain Diophantine triples. (English) Zbl 1475.11046 J. Number Theory 210, 433-475 (2020). Reviewer: Volker Ziegler (Salzburg) MSC: 11D09 11B37 11J86 PDF BibTeX XML Cite \textit{M. Cipu} et al., J. Number Theory 210, 433--475 (2020; Zbl 1475.11046) Full Text: DOI OpenURL
Deng, Nai-Juan; Wu, Dan-Yao; Yuan, Ping-Zhi The exponential Diophantine equation \((3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z\). (English) Zbl 1448.11071 Turk. J. Math. 43, No. 5, 2561-2567 (2019). MSC: 11D61 PDF BibTeX XML Cite \textit{N.-J. Deng} et al., Turk. J. Math. 43, No. 5, 2561--2567 (2019; Zbl 1448.11071) Full Text: Link OpenURL
Bennett, Michael A.; Patel, Vandita; Siksek, Samir Shifted powers in Lucas-Lehmer sequences. (English) Zbl 1435.11067 Res. Number Theory 5, No. 1, Paper No. 15, 27 p. (2019). Reviewer: Florian Luca (Johannesburg) MSC: 11D61 11D41 11F80 11F41 PDF BibTeX XML Cite \textit{M. A. Bennett} et al., Res. Number Theory 5, No. 1, Paper No. 15, 27 p. (2019; Zbl 1435.11067) Full Text: DOI arXiv OpenURL
Erazo, Harold S.; Gómez, Carlos A.; Luca, Florian On Pillai’s problem with \(X\)-coordinates of Pell equations and powers of 2. (English) Zbl 1465.11086 J. Number Theory 203, 294-309 (2019). Reviewer: Ilker Inam (Bilecik) MSC: 11D61 11B39 11D45 PDF BibTeX XML Cite \textit{H. S. Erazo} et al., J. Number Theory 203, 294--309 (2019; Zbl 1465.11086) Full Text: DOI OpenURL
Fu, Ruiqin; He, Bo; Yang, Hai; Zhu, Huilin On some ternary pure exponential Diophantine equations with three consecutive positive integers bases. (English) Zbl 1428.11059 Proc. Indian Acad. Sci., Math. Sci. 129, No. 2, Paper No. 26, 12 p. (2019). MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{R. Fu} et al., Proc. Indian Acad. Sci., Math. Sci. 129, No. 2, Paper No. 26, 12 p. (2019; Zbl 1428.11059) Full Text: DOI OpenURL
Bilu, Yuri; Marques, Diego; Togbé, Alain Generalized Cullen numbers in linear recurrence sequences. (English) Zbl 1446.11023 J. Number Theory 202, 412-425 (2019). Reviewer: Antonio M. Oller Marcén (Zaragoza) MSC: 11B37 11B39 11J86 PDF BibTeX XML Cite \textit{Y. Bilu} et al., J. Number Theory 202, 412--425 (2019; Zbl 1446.11023) Full Text: DOI arXiv OpenURL
Szikszai, Márton; Ziegler, Volker On arithmetic progressions in Lucas sequences. II. (English) Zbl 1473.11027 J. Number Theory 201, 354-376 (2019). MSC: 11B25 11D61 11B39 PDF BibTeX XML Cite \textit{M. Szikszai} and \textit{V. Ziegler}, J. Number Theory 201, 354--376 (2019; Zbl 1473.11027) Full Text: DOI OpenURL
Rihane, Salah Eddine; Hernane, Mohand Ouamar; Togbé, Alain The \(X\)-coordinates of Pell equations and Padovan numbers. (English) Zbl 1448.11069 Turk. J. Math. 43, No. 1, 207-223 (2019). MSC: 11D09 11A25 11B39 11J86 PDF BibTeX XML Cite \textit{S. E. Rihane} et al., Turk. J. Math. 43, No. 1, 207--223 (2019; Zbl 1448.11069) Full Text: DOI OpenURL
He, Bo; Togbé, Alain; Ziegler, Volker There is no Diophantine quintuple. (English) Zbl 1430.11044 Trans. Am. Math. Soc. 371, No. 9, 6665-6709 (2019). MSC: 11D09 11J86 11Y50 11J68 PDF BibTeX XML Cite \textit{B. He} et al., Trans. Am. Math. Soc. 371, No. 9, 6665--6709 (2019; Zbl 1430.11044) Full Text: DOI arXiv OpenURL
Bliznac Trebješanin, Marija; Filipin, Alan Nonexistence of \(D(4)\)-quintuples. (English) Zbl 1434.11077 J. Number Theory 194, 170-217 (2019). MSC: 11D09 11D45 11J86 PDF BibTeX XML Cite \textit{M. Bliznac Trebješanin} and \textit{A. Filipin}, J. Number Theory 194, 170--217 (2019; Zbl 1434.11077) Full Text: DOI arXiv OpenURL
He, Bo; Pu, Keli; Shen, Rulin; Togbé, Alain A note on the regularity of the Diophantine pair \(\{k, 4k \pm 4 \}\). (English. French summary) Zbl 1446.11050 J. Théor. Nombres Bordx. 30, No. 3, 879-892 (2018). Reviewer: István Gaál (Debrecen) MSC: 11D09 11B37 11J68 11J86 11Y65 PDF BibTeX XML Cite \textit{B. He} et al., J. Théor. Nombres Bordx. 30, No. 3, 879--892 (2018; Zbl 1446.11050) Full Text: DOI OpenURL
Kizildere, Elif; Miyazaki, Takafumi; Soydan, Gökhan On the Diophantine equation \(((c+1)m^{2}+1)^{x}+(cm^{2}-1)^{y}=(am)^z\). (English) Zbl 1424.11084 Turk. J. Math. 42, No. 5, 2690-2698 (2018). MSC: 11D61 PDF BibTeX XML Cite \textit{E. Kizildere} et al., Turk. J. Math. 42, No. 5, 2690--2698 (2018; Zbl 1424.11084) Full Text: DOI OpenURL
Alan, Murat On the exponential Diophantine equation \((18m^2+1)^x+(7m^2-1)^y=(5m)^z\). (English) Zbl 1424.11079 Turk. J. Math. 42, No. 4, 1990-1999 (2018). MSC: 11D61 11D75 PDF BibTeX XML Cite \textit{M. Alan}, Turk. J. Math. 42, No. 4, 1990--1999 (2018; Zbl 1424.11079) Full Text: DOI OpenURL
Cipu, Mihai; Fujita, Yasutsugu; Mignotte, Maurice Two-parameter families of uniquely extendable Diophantine triples. (English) Zbl 1419.11054 Sci. China, Math. 61, No. 3, 421-438 (2018). MSC: 11D09 11B37 11J68 11J86 PDF BibTeX XML Cite \textit{M. Cipu} et al., Sci. China, Math. 61, No. 3, 421--438 (2018; Zbl 1419.11054) Full Text: DOI arXiv OpenURL
Cipu, Mihai; Fujita, Yasutsugu; Miyazaki, Takafumi On the number of extensions of a Diophantine triple. (English) Zbl 1429.11065 Int. J. Number Theory 14, No. 3, 899-917 (2018). MSC: 11D45 11D09 11B37 11J86 PDF BibTeX XML Cite \textit{M. Cipu} et al., Int. J. Number Theory 14, No. 3, 899--917 (2018; Zbl 1429.11065) Full Text: DOI OpenURL
Fujita, Yasutsugu; Miyazaki, Takafumi The regularity of Diophantine quadruples. (English) Zbl 1417.11024 Trans. Am. Math. Soc. 370, No. 6, 3803-3831 (2018). MSC: 11D45 11D09 11B37 11J68 11J86 PDF BibTeX XML Cite \textit{Y. Fujita} and \textit{T. Miyazaki}, Trans. Am. Math. Soc. 370, No. 6, 3803--3831 (2018; Zbl 1417.11024) Full Text: DOI OpenURL
Bérczes, Attila; Pink, István; Savaş, Gamze; Soydan, Gökhan On the Diophantine equation \((x+1)^{k}+(x+2)^{k}+\ldots+(2x)^{k}=y^{n}\). (English) Zbl 1433.11034 J. Number Theory 183, 326-351 (2018). MSC: 11D61 11D41 11J86 PDF BibTeX XML Cite \textit{A. Bérczes} et al., J. Number Theory 183, 326--351 (2018; Zbl 1433.11034) Full Text: DOI arXiv OpenURL
Hu, Yongzhong; Le, Maohua An upper bound for the number of solutions of ternary purely exponential Diophantine equations. (English) Zbl 1433.11036 J. Number Theory 183, 62-73 (2018). MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{Y. Hu} and \textit{M. Le}, J. Number Theory 183, 62--73 (2018; Zbl 1433.11036) Full Text: DOI arXiv OpenURL
He, Bo; Pintér, Ákos; Togbé, Alain; Yang, Shichun Another generalization of a theorem of Baker and Davenport. (English) Zbl 1430.11043 J. Number Theory 182, 325-343 (2018). Reviewer: Volker Ziegler (Salzburg) MSC: 11D09 11D45 11B37 11J86 PDF BibTeX XML Cite \textit{B. He} et al., J. Number Theory 182, 325--343 (2018; Zbl 1430.11043) Full Text: DOI arXiv OpenURL
Terai, Nobuhiro; Hibino, Takeshi On the exponential Diophantine equation \((3pm^2-1)^x + ( p( p - 3)m^2 + 1)^y = (pm)^z\). (English) Zbl 1399.11104 Period. Math. Hung. 74, No. 2, 227-234 (2017). MSC: 11D61 PDF BibTeX XML Cite \textit{N. Terai} and \textit{T. Hibino}, Period. Math. Hung. 74, No. 2, 227--234 (2017; Zbl 1399.11104) Full Text: DOI OpenURL
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 OpenURL
Deng, Mou-Jie; Huang, Dong-Ming A note on Jeśmanowicz’ conjecture concerning primitive Pythagorean triples. (English) Zbl 1431.11046 Bull. Aust. Math. Soc. 95, No. 1, 5-13 (2017). MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{M.-J. Deng} and \textit{D.-M. Huang}, Bull. Aust. Math. Soc. 95, No. 1, 5--13 (2017; Zbl 1431.11046) Full Text: DOI OpenURL
Bennett, Michael A.; Patel, Vandita; Siksek, Samir Perfect powers that are sums of consecutive cubes. (English) Zbl 1437.11046 Mathematika 63, No. 1, 230-249 (2017). MSC: 11D25 11D85 11J86 11F80 PDF BibTeX XML Cite \textit{M. A. Bennett} et al., Mathematika 63, No. 1, 230--249 (2017; Zbl 1437.11046) Full Text: DOI arXiv OpenURL
Miyazaki, T.; Togbé, A.; Yuan, P. On the Diophantine equation \(a^x+b^y=(a+2)^z\). (English) Zbl 1389.11088 Acta Math. Hung. 149, No. 1, 1-9 (2016). Reviewer: Lajos Hajdu (Debrecen) MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{T. Miyazaki} et al., Acta Math. Hung. 149, No. 1, 1--9 (2016; Zbl 1389.11088) Full Text: DOI OpenURL
He, Bo; Luca, Florian; Togbé, Alain Diophantine triples of Fibonacci numbers. (English) Zbl 1359.11028 Acta Arith. 175, No. 1, 57-70 (2016). Reviewer: Volker Ziegler (Salzburg) MSC: 11D09 11D45 11B39 11J86 PDF BibTeX XML Cite \textit{B. He} et al., Acta Arith. 175, No. 1, 57--70 (2016; Zbl 1359.11028) Full Text: DOI OpenURL
Marques, Diego; Trojovský, Pavel Terms of generalized Fibonacci sequences that are powers of their orders. (English) Zbl 1403.11027 Lith. Math. J. 56, No. 2, 219-228 (2016). MSC: 11D61 11B39 11J86 PDF BibTeX XML Cite \textit{D. Marques} and \textit{P. Trojovský}, Lith. Math. J. 56, No. 2, 219--228 (2016; Zbl 1403.11027) Full Text: DOI OpenURL
Hajdu, Lajos; Laishram, Shanta; Tengely, Szabolcs Power values of sums of products of consecutive integers. (English) Zbl 1400.11087 Acta Arith. 172, No. 4, 333-349 (2016). Reviewer: Volker Ziegler (Salzburg) MSC: 11D41 11D25 PDF BibTeX XML Cite \textit{L. Hajdu} et al., Acta Arith. 172, No. 4, 333--349 (2016; Zbl 1400.11087) Full Text: DOI Link OpenURL
Bérczes, A.; Hajdu, L.; Miyazaki, T.; Pink, I. On the equation \(1^{k}+2^{k}+\cdots +x^{k}=y^{n}\) for fixed \(x\). (English) Zbl 1402.11052 J. Number Theory 163, 43-60 (2016). MSC: 11D61 11D41 PDF BibTeX XML Cite \textit{A. Bérczes} et al., J. Number Theory 163, 43--60 (2016; Zbl 1402.11052) Full Text: DOI OpenURL
Bennett, Michael A.; Dahmen, Sander R.; Mignotte, Maurice; Siksek, Samir Shifted powers in binary recurrence sequences. (English) Zbl 1371.11081 Math. Proc. Camb. Philos. Soc. 158, No. 2, 305-329 (2015). MSC: 11D61 11B37 11J86 11G05 PDF BibTeX XML Cite \textit{M. A. Bennett} et al., Math. Proc. Camb. Philos. Soc. 158, No. 2, 305--329 (2015; Zbl 1371.11081) Full Text: DOI arXiv OpenURL
Miyazaki, T.; Terai, N. On Jeśmanowicz’ conjecture concerning primitive Pythagorean triples. II. (English) Zbl 1374.11056 Acta Math. Hung. 147, No. 2, 286-293 (2015). Reviewer: Attila Bérczes (Debrecen) MSC: 11D61 11D41 PDF BibTeX XML Cite \textit{T. Miyazaki} and \textit{N. Terai}, Acta Math. Hung. 147, No. 2, 286--293 (2015; Zbl 1374.11056) Full Text: DOI OpenURL
Hu, Yongzhong; Le, Maohua A note on ternary purely exponential Diophantine equations. (English) Zbl 1379.11030 Acta Arith. 171, No. 2, 173-182 (2015). MSC: 11D61 11D45 PDF BibTeX XML Cite \textit{Y. Hu} and \textit{M. Le}, Acta Arith. 171, No. 2, 173--182 (2015; Zbl 1379.11030) Full Text: DOI OpenURL
He, Bo; Pintér, Ákos; Togbé, Alain On simultaneous Pell equations and related Thue equations. (English) Zbl 1378.11041 Proc. Am. Math. Soc. 143, No. 11, 4685-4693 (2015). MSC: 11D09 11D45 11B37 11J86 PDF BibTeX XML Cite \textit{B. He} et al., Proc. Am. Math. Soc. 143, No. 11, 4685--4693 (2015; Zbl 1378.11041) Full Text: DOI Link OpenURL
Marques, Diego Generalized Fibonacci numbers of the form \(2^a + 3^b + 5^c\). (English) Zbl 1366.11030 Bull. Braz. Math. Soc. (N.S.) 45, No. 3, 543-557 (2014). MSC: 11B39 11J86 PDF BibTeX XML Cite \textit{D. Marques}, Bull. Braz. Math. Soc. (N.S.) 45, No. 3, 543--557 (2014; Zbl 1366.11030) Full Text: DOI OpenURL
Hajdu, Lajos; Pink, István On the Diophantine equation \(1 + 2^a + x^b = y^n\). (English) Zbl 1353.11060 J. Number Theory 143, 1-13 (2014). MSC: 11D41 11D61 PDF BibTeX XML Cite \textit{L. Hajdu} and \textit{I. Pink}, J. Number Theory 143, 1--13 (2014; Zbl 1353.11060) Full Text: DOI OpenURL
Terai, Nobuhiro On Jeśmanowicz’ conjecture concerning primitive Pythagorean triples. (English) Zbl 1309.11030 J. Number Theory 141, 316-323 (2014). MSC: 11D61 PDF BibTeX XML Cite \textit{N. Terai}, J. Number Theory 141, 316--323 (2014; Zbl 1309.11030) Full Text: DOI OpenURL
Miyazaki, Takafumi; Yuan, Pingzhi; Wu, Danyao Generalizations of classical results on Jeśmanowicz’ conjecture concerning Pythagorean triples. II. (English) Zbl 1310.11040 J. Number Theory 141, 184-201 (2014). MSC: 11D61 11J86 11D09 PDF BibTeX XML Cite \textit{T. Miyazaki} et al., J. Number Theory 141, 184--201 (2014; Zbl 1310.11040) Full Text: DOI OpenURL
Miyazaki, Takafumi; Terai, Nobuhiro On the exponential Diophantine equation \((m^2 + 1)^x + (cm^2 - 1)^y = (am)^z\). (English) Zbl 1334.11019 Bull. Aust. Math. Soc. 90, No. 1, 9-19 (2014). MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{T. Miyazaki} and \textit{N. Terai}, Bull. Aust. Math. Soc. 90, No. 1, 9--19 (2014; Zbl 1334.11019) Full Text: DOI OpenURL
Marques, Diego; Togbé, Alain Fibonacci and Lucas numbers of the form \(2^a+3^b+5^c\). (English) Zbl 1362.11018 Proc. Japan Acad., Ser. A 89, No. 3, 47-50 (2013). MSC: 11B39 11J86 PDF BibTeX XML Cite \textit{D. Marques} and \textit{A. Togbé}, Proc. Japan Acad., Ser. A 89, No. 3, 47--50 (2013; Zbl 1362.11018) Full Text: DOI Euclid OpenURL
Miyazaki, Takafumi Generalizations of classical results on Jeśmanowicz’ conjecture concerning Pythagorean triples. (English) Zbl 1309.11029 J. Number Theory 133, No. 2, 583-595 (2013). MSC: 11D61 11D41 11J86 PDF BibTeX XML Cite \textit{T. Miyazaki}, J. Number Theory 133, No. 2, 583--595 (2013; Zbl 1309.11029) Full Text: DOI OpenURL
Bennett, Michael A.; Bugeaud, Yann; Mignotte, Maurice Perfect powers with few binary digits and related Diophantine problems. II. (English) Zbl 1291.11016 Math. Proc. Camb. Philos. Soc. 153, No. 3, 525-540 (2012). Reviewer: Thomas Stoll (Vandœuvre-lés Nancy) MSC: 11A63 11D61 11J86 PDF BibTeX XML Cite \textit{M. A. Bennett} et al., Math. Proc. Camb. Philos. Soc. 153, No. 3, 525--540 (2012; Zbl 1291.11016) Full Text: DOI OpenURL
Miyazaki, T.; Togbé, A. The Diophantine equation \((2am - 1)^x + (2m)^y = (2am + 1)^z\). (English) Zbl 1290.11068 Int. J. Number Theory 8, No. 8, 2035-2044 (2012). Reviewer: Gökhan Soydan (Bursa) MSC: 11D61 PDF BibTeX XML Cite \textit{T. Miyazaki} and \textit{A. Togbé}, Int. J. Number Theory 8, No. 8, 2035--2044 (2012; Zbl 1290.11068) Full Text: DOI OpenURL
Cipu, Mihai; Mignotte, Maurice; Togbé, Alain On the size of the intersection of two Lucas sequences of distinct type. II. (English) Zbl 1252.11030 Sci. China, Math. 54, No. 7, 1299-1316 (2011). Reviewer: Florian Luca (Morelia) MSC: 11D61 11Y50 11J70 PDF BibTeX XML Cite \textit{M. Cipu} et al., Sci. China, Math. 54, No. 7, 1299--1316 (2011; Zbl 1252.11030) Full Text: DOI OpenURL
Laradji, A.; Mignotte, M.; Tzanakis, N. On \(px^{2}+q^{2n}=y^{p}\) and related Diophantine equations. (English) Zbl 1229.11055 J. Number Theory 131, No. 9, 1575-1596 (2011). Reviewer: Alain Kraus (Paris) MSC: 11D61 PDF BibTeX XML Cite \textit{A. Laradji} et al., J. Number Theory 131, No. 9, 1575--1596 (2011; Zbl 1229.11055) Full Text: DOI arXiv OpenURL
Marques, Diego; Togbé, Alain On the sum of powers of two consecutive Fibonacci numbers. (English) Zbl 1222.11024 Proc. Japan Acad., Ser. A 86, No. 10, 174-176 (2010). Reviewer: Florin Nicolae (Berlin) MSC: 11B39 PDF BibTeX XML Cite \textit{D. Marques} and \textit{A. Togbé}, Proc. Japan Acad., Ser. A 86, No. 10, 174--176 (2010; Zbl 1222.11024) Full Text: DOI OpenURL