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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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 $2^ n+px^ 2=y^ p$
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by Mao Hua Le PDF
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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • 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