A Note on Terai's Conjecture Concerning the Exponential Diophantine Equation x^{2}+b^{y}=c^{z}
Number Theory
2021-06-01 v1
Abstract
Let (a,b,c) be a primitive Pythagorean triple, i.e., a^{2}+b^{2}=c^{2} with gcd(a,b,c)=1, a even and b odd. Terai's conjecture says that the Diophantine equation x^{2}+b^{y}=c^{z} has only the positive integer solutions (x,y,z)=(a,2,2). In this study, we prove that Terai's conjecture is true when b is a product of two primes and c=5(mod8).
Keywords
Cite
@article{arxiv.2105.14814,
title = {A Note on Terai's Conjecture Concerning the Exponential Diophantine Equation x^{2}+b^{y}=c^{z}},
author = {Refik Keskin and Zafer Şiar},
journal= {arXiv preprint arXiv:2105.14814},
year = {2021}
}