A NOTE ON THE DIOPHANTINE EQUATIONSx2 pn= yn

Yıl 2018, Cilt: 67 Sayı: 1, 317 - 322, 01.02.2018

Gökhan Soydan

https://doi.org/10.1501/Commua1_0000000853

Cited By: 1

Anahtar Kelimeler

Exponential Diophantine equation, Frey curve

Kaynakça

• 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 : [e-mail] ORCID: http://orcid.org/0000-0002-6321-4132