On the Diophantine equation X^{2N} + 2^{2 alpha} 5^{2 beta} p^{2 gamma} = Z^5
Number Theory
2014-09-09 v1
Abstract
We prove that for each odd prime p, positive integer alpha, and non-negative integers beta and gamma, the Diophantine equation X^{2N} + 2^{2 alpha} 5^{2 beta} p^{2 gamma} = Z^5 has no solution with X, Z, N in Z^+, N > 1, and gcd(X,Z) = 1.
Keywords
Cite
@article{arxiv.1409.2463,
title = {On the Diophantine equation X^{2N} + 2^{2 alpha} 5^{2 beta} p^{2 gamma} = Z^5},
author = {Eva G. Goedhart and Helen G. Grundman},
journal= {arXiv preprint arXiv:1409.2463},
year = {2014}
}