On the Diophantine equation 2ⁿ+𝑝𝑥²=𝑦^{𝑝}

Le, Mao Hua

doi:10.1090/S0002-9939-1995-1215203-4

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

Author: Mao Hua Le
Journal: Proc. Amer. Math. Soc. 123 (1995), 321-326
MSC: Primary 11D61; Secondary 11J86
DOI: https://doi.org/10.1090/S0002-9939-1995-1215203-4
MathSciNet review: 1215203
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Abstract: Let p be a prime with . 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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