Open Access
December 2010 On the diophantine equation $x^{2}+5^{a}\cdot 11^{b}=y^{n}$
Musa Demirci, İsmail Naci Cangül, Gökhan Soydan, Nikos Tzanakis
Funct. Approx. Comment. Math. 43(2): 209-225 (December 2010). DOI: 10.7169/facm/1291903397

Abstract

We give the complete solution $(n,a,b,x,y)$ of the title equation when $\gcd(x,y)=1$, except for the case when $xab$ is odd. Our main result is Theorem 1.

Citation

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Musa Demirci. İsmail Naci Cangül. Gökhan Soydan. Nikos Tzanakis. "On the diophantine equation $x^{2}+5^{a}\cdot 11^{b}=y^{n}$." Funct. Approx. Comment. Math. 43 (2) 209 - 225, December 2010. https://doi.org/10.7169/facm/1291903397

Information

Published: December 2010
First available in Project Euclid: 9 December 2010

zbMATH: 1237.11019
MathSciNet: MR2767170
Digital Object Identifier: 10.7169/facm/1291903397

Subjects:
Primary: 11D61
Secondary: 11D25 , 11D41 , 11D59 , 11J86

Keywords: $S$-Integral points of an elliptic curve , exponential Diophantine equation , Linear form in logarithms of algebraic numbers , Lucas sequence , Thue-Mahler equation

Rights: Copyright © 2010 Adam Mickiewicz University

Vol.43 • No. 2 • December 2010
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