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.
Publié le : 2010-12-15
Classification:
Exponential Diophantine equation,
$S$-Integral points of an elliptic curve,
Thue-Mahler equation,
Lucas sequence,
Linear form in logarithms of algebraic numbers,
11D61,
11D25,
11D41,
11D59,
11J86
@article{1291903397,
author = {Naci Cang\"ul, \.Ismail and Demirci, Musa and Soydan, G\"okhan and Tzanakis, Nikos},
title = {On the diophantine equation $x^{2}+5^{a}\cdot 11^{b}=y^{n}$},
journal = {Funct. Approx. Comment. Math.},
volume = {42},
number = {1},
year = {2010},
pages = { 209-225},
language = {en},
url = {http://dml.mathdoc.fr/item/1291903397}
}
Naci Cangül, İsmail; Demirci, Musa; Soydan, Gökhan; Tzanakis, Nikos. On the diophantine equation $x^{2}+5^{a}\cdot 11^{b}=y^{n}$. Funct. Approx. Comment. Math., Tome 42 (2010) no. 1, pp. 209-225. http://gdmltest.u-ga.fr/item/1291903397/