A note on the Diophantine equations x²±5^α⋅ pⁿ=yⁿ

2017/06/10 by Soydan, Gökhan
#11D61 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1706.03185

Abstract

Suppose that x is odd, n≥7 and p∉\2,5\ are primes. In this paper, we prove that the Diophantine equations x²±5^αpⁿ=yⁿ have no solutions in positive integers α,x,y with gcd(x,y)=1.

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