# Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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## On the Diophantine equation $2^ n+px^ 2=y^ p$HTML articles powered by AMS MathViewer

by Mao Hua Le
Proc. Amer. Math. Soc. 123 (1995), 321-326 Request permission

## Abstract:

Let p be a prime with $p > 3$. In this paper we prove that: (i) the equation ${2^n} + p{x^2} = {y^p}$ has no positive integer solution (x, y, n) with $\gcd (x,y) = 1$; (ii) if $p \nequiv 7 \pmod 8$, then the equation has no positive integer solution (x, y, n).
References
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