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A NOTE ON THE DIOPHANTINE EQUATIONSx2 pn= yn

Year 2018, Volume: 67 Issue: 1, 317 - 322, 01.02.2018
https://doi.org/10.1501/Commua1_0000000853

References

  • Arif, S. A. and Abu Muriefah, F. S., On the Diophantine equation x2+ q2k+1= yn, J. Number Theo. (2002), 95 (1), 95-100.
  • Abu Muriefah, F.S. and Bugeaud, Y., The Diophantine equation x2+ C = yn: a brief overview, Revis. Col. Math. (2006), 40 (1), 31-37.
  • Bennett, M.A. and Skinner, C., Ternary Diophantine equations via Galois representations and modular forms, Canad. J. Math. (2004), 56 (1), 23-54.
  • Berczés, A. and Pink, I., On generalized Lebesgue-Ramanujan-Nagell equations, An. ¸St. Univ. Ovid. Cons. (2014), 22 (1), 51-71.
  • Cangul, I.N., Demirci, M., Luca, F., Inam, I. and Soydan, G., On the Diophantine equation x2+ 2a3b11c= yn, Math. Slovaca (2013), 63 (3), 647-659.
  • Cangul, I.N., Demirci, M., Luca, F., Pintér, Á. and Soydan, G., On the Diophantine equation x2+ 2a11b= yn, Fibonacci Quart. (2010), 48 (1), 39-46.
  • Cangul, I.N., Demirci, M., Soydan, G. and Tzanakis, N., On the Diophantine equation x2+ a11b= yn, Funct. Approx. (2010), (43) 2, 209-225.
  • Cohen,H., Number Theory Vol. II: Analytic and Modern Tools, Springer, 2007.
  • Dabrowski, A. On the Lebesgue-Nagell equation, Colloq. Math. (2011), 125 (2), 245-253.
  • Darmon, H. and Merel, L., Winding quotients and some variants of Fermat’s Last Theorem, Jour. für die reine und ang. Math. (1997), 490, 81-100.
  • Godinho, H., Marques, D. and Togbé, A., On the Diophantine equation x2+ 2 5 17 = yn, Com. in Math. (2012), 20 (2), 81-88.
  • Godinho, H., Marques, D. and Togbé, A., On the Diophantine equation x2+ C = yn, C = 2:3:17, C = 2:13:17, Math. Slovaca (2016), 66 (3), 1-10.
  • Goins, E., Luca, F. and Togbé, A., On the Diophantine equation x2+ 2 5 13 = yn, ANTS VIII Proc. (2008), 5011, 430-442.
  • Ivorra, W. and Kraus, A., Quelques résultats sur les équations axp+ byp= cz2, Canad. J. Math. (2006), 58 (1), 115-153.
  • Luca, F., On the Diophantine equation x2+ 2a3b= yn, Int. J. Math. Sci. (2002), 29 (4), 244.
  • Guo, Y. and Le, M. H., A note on the exponential Diophantin equation x2 m= yn, Proc. Amer. Math. Soc. (1995), 123 (12), 3627-3629.
  • Luca, F. and Togbé, A., On the Diophantine equation x2+ 2a5b= yn, Int. J. Num. Th. (2008), 4 (6), 973-979.
  • Abu Muriefah, F.S., Luca, F. and Togbé, A., On the Diophantine equation x2+ 5a13b= yn, Glasgow Math. J. (2008), 50 (1), 175-181.
  • Luca, F. and Togbé, A. On the Diophantine equation x2+ 2a13b= yn, Colloq. Math. (2009), (1), 139-146.
  • Pink, I., On the Diophantine equation x2+ 2 3 5 7 = yn, Publ. Math. Deb. 70 (2007), 70 (1-2), 149-166.
  • Pink, I. and Rábai, Z., On the Diophantine equation x2+ 5k17l= yn, Comm. in Math. (2011), 19 (1), 1-9.
  • Ribet, K.A., On modular representations of Gal(Q=Q) arising from modular forms, Invent. Mat. (1990), 100 (2), 431-476.
  • Siksek, S., The modular approach to Diophantine equations, Panoramas & Synthèses (2012), , 151-179.
  • Soydan, G., On the Diophantine equation x2+ 7 11 = yn, Miskolc Math. Notes (2012), 13 (2), 515-527.
  • Soydan, G. and Tzanakis, N., Complete solution of the Diophantine equation x2+5a11b= yn, Bull. of the Hellenic Math. Soc. (2016), 60, 125-151.
  • Soydan, G., Ulas, M. and Zhu, H., On the Diophantine equation x2+ 2a19b= yn, Indian J. Pure and App. Math. (2012), 43 (3), 251-261.
  • Wiles, A., Modular elliptic curves and Fermat’s Last Theorem, Ann. of Math. (1995), 141. (3), 443-551.
  • Zhu, H., Le, M.H., Soydan, G. and Togbé, A., On the exponential Diophantine equation x2+ 2apb= yn, Periodica Math. Hung. (2015), 70 (2), 233-247.
  • Current address : Gökhan Soydan: Department of Mathematics, Uluda¼g University, 16059 Bursa-TURKEY
  • E-mail address : gsoydan@uludag.edu.tr ORCID: http://orcid.org/0000-0002-6321-4132
Year 2018, Volume: 67 Issue: 1, 317 - 322, 01.02.2018
https://doi.org/10.1501/Commua1_0000000853

References

  • Arif, S. A. and Abu Muriefah, F. S., On the Diophantine equation x2+ q2k+1= yn, J. Number Theo. (2002), 95 (1), 95-100.
  • Abu Muriefah, F.S. and Bugeaud, Y., The Diophantine equation x2+ C = yn: a brief overview, Revis. Col. Math. (2006), 40 (1), 31-37.
  • Bennett, M.A. and Skinner, C., Ternary Diophantine equations via Galois representations and modular forms, Canad. J. Math. (2004), 56 (1), 23-54.
  • Berczés, A. and Pink, I., On generalized Lebesgue-Ramanujan-Nagell equations, An. ¸St. Univ. Ovid. Cons. (2014), 22 (1), 51-71.
  • Cangul, I.N., Demirci, M., Luca, F., Inam, I. and Soydan, G., On the Diophantine equation x2+ 2a3b11c= yn, Math. Slovaca (2013), 63 (3), 647-659.
  • Cangul, I.N., Demirci, M., Luca, F., Pintér, Á. and Soydan, G., On the Diophantine equation x2+ 2a11b= yn, Fibonacci Quart. (2010), 48 (1), 39-46.
  • Cangul, I.N., Demirci, M., Soydan, G. and Tzanakis, N., On the Diophantine equation x2+ a11b= yn, Funct. Approx. (2010), (43) 2, 209-225.
  • Cohen,H., Number Theory Vol. II: Analytic and Modern Tools, Springer, 2007.
  • Dabrowski, A. On the Lebesgue-Nagell equation, Colloq. Math. (2011), 125 (2), 245-253.
  • Darmon, H. and Merel, L., Winding quotients and some variants of Fermat’s Last Theorem, Jour. für die reine und ang. Math. (1997), 490, 81-100.
  • Godinho, H., Marques, D. and Togbé, A., On the Diophantine equation x2+ 2 5 17 = yn, Com. in Math. (2012), 20 (2), 81-88.
  • Godinho, H., Marques, D. and Togbé, A., On the Diophantine equation x2+ C = yn, C = 2:3:17, C = 2:13:17, Math. Slovaca (2016), 66 (3), 1-10.
  • Goins, E., Luca, F. and Togbé, A., On the Diophantine equation x2+ 2 5 13 = yn, ANTS VIII Proc. (2008), 5011, 430-442.
  • Ivorra, W. and Kraus, A., Quelques résultats sur les équations axp+ byp= cz2, Canad. J. Math. (2006), 58 (1), 115-153.
  • Luca, F., On the Diophantine equation x2+ 2a3b= yn, Int. J. Math. Sci. (2002), 29 (4), 244.
  • Guo, Y. and Le, M. H., A note on the exponential Diophantin equation x2 m= yn, Proc. Amer. Math. Soc. (1995), 123 (12), 3627-3629.
  • Luca, F. and Togbé, A., On the Diophantine equation x2+ 2a5b= yn, Int. J. Num. Th. (2008), 4 (6), 973-979.
  • Abu Muriefah, F.S., Luca, F. and Togbé, A., On the Diophantine equation x2+ 5a13b= yn, Glasgow Math. J. (2008), 50 (1), 175-181.
  • Luca, F. and Togbé, A. On the Diophantine equation x2+ 2a13b= yn, Colloq. Math. (2009), (1), 139-146.
  • Pink, I., On the Diophantine equation x2+ 2 3 5 7 = yn, Publ. Math. Deb. 70 (2007), 70 (1-2), 149-166.
  • Pink, I. and Rábai, Z., On the Diophantine equation x2+ 5k17l= yn, Comm. in Math. (2011), 19 (1), 1-9.
  • Ribet, K.A., On modular representations of Gal(Q=Q) arising from modular forms, Invent. Mat. (1990), 100 (2), 431-476.
  • Siksek, S., The modular approach to Diophantine equations, Panoramas & Synthèses (2012), , 151-179.
  • Soydan, G., On the Diophantine equation x2+ 7 11 = yn, Miskolc Math. Notes (2012), 13 (2), 515-527.
  • Soydan, G. and Tzanakis, N., Complete solution of the Diophantine equation x2+5a11b= yn, Bull. of the Hellenic Math. Soc. (2016), 60, 125-151.
  • Soydan, G., Ulas, M. and Zhu, H., On the Diophantine equation x2+ 2a19b= yn, Indian J. Pure and App. Math. (2012), 43 (3), 251-261.
  • Wiles, A., Modular elliptic curves and Fermat’s Last Theorem, Ann. of Math. (1995), 141. (3), 443-551.
  • Zhu, H., Le, M.H., Soydan, G. and Togbé, A., On the exponential Diophantine equation x2+ 2apb= yn, Periodica Math. Hung. (2015), 70 (2), 233-247.
  • Current address : Gökhan Soydan: Department of Mathematics, Uluda¼g University, 16059 Bursa-TURKEY
  • E-mail address : gsoydan@uludag.edu.tr ORCID: http://orcid.org/0000-0002-6321-4132
There are 30 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Gökhan Soydan This is me

Publication Date February 1, 2018
Published in Issue Year 2018 Volume: 67 Issue: 1

Cite

APA Soydan, G. (2018). A NOTE ON THE DIOPHANTINE EQUATIONSx2 pn= yn. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(1), 317-322. https://doi.org/10.1501/Commua1_0000000853
AMA Soydan G. A NOTE ON THE DIOPHANTINE EQUATIONSx2 pn= yn. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2018;67(1):317-322. doi:10.1501/Commua1_0000000853
Chicago Soydan, Gökhan. “A NOTE ON THE DIOPHANTINE EQUATIONSx2 Pn= Yn”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67, no. 1 (February 2018): 317-22. https://doi.org/10.1501/Commua1_0000000853.
EndNote Soydan G (February 1, 2018) A NOTE ON THE DIOPHANTINE EQUATIONSx2 pn= yn. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67 1 317–322.
IEEE G. Soydan, “A NOTE ON THE DIOPHANTINE EQUATIONSx2 pn= yn”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 67, no. 1, pp. 317–322, 2018, doi: 10.1501/Commua1_0000000853.
ISNAD Soydan, Gökhan. “A NOTE ON THE DIOPHANTINE EQUATIONSx2 Pn= Yn”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67/1 (February 2018), 317-322. https://doi.org/10.1501/Commua1_0000000853.
JAMA Soydan G. A NOTE ON THE DIOPHANTINE EQUATIONSx2 pn= yn. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67:317–322.
MLA Soydan, Gökhan. “A NOTE ON THE DIOPHANTINE EQUATIONSx2 Pn= Yn”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 67, no. 1, 2018, pp. 317-22, doi:10.1501/Commua1_0000000853.
Vancouver Soydan G. A NOTE ON THE DIOPHANTINE EQUATIONSx2 pn= yn. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67(1):317-22.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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