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On the Diophantine equation $2^ n+px^ 2=y^ p$

Author: Mao Hua Le
Journal: Proc. Amer. Math. Soc. 123 (1995), 321-326
MSC: Primary 11D61; Secondary 11J86
MathSciNet review: 1215203
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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).

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Article copyright: © Copyright 1995 American Mathematical Society