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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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The Diophantine equation $x^ 2=4q^ n+4q^ m+1$
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by Mao Hua Le PDF
Proc. Amer. Math. Soc. 106 (1989), 599-604 Request permission

Abstract:

Let $q = {p^r}$ be a prime power. In this paper, we prove that the equation ${x^2} = 4{q^n} + 4{q^m} + 1,m < n,{\text {g}}{\text {.c}}{\text {.d}}{\text {.}}(m,n) = 1$ has no positive integer solution $(m,n,x)$ with $m > 2$.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 106 (1989), 599-604
  • MSC: Primary 11D61
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0968624-6
  • MathSciNet review: 968624