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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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A note on the equation $x^{2}=y^{q}+1$
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by E. Z. Chein PDF
Proc. Amer. Math. Soc. 56 (1976), 83-84 Request permission

Abstract:

It is proved here that the equation ${x^2} = {y^q} + 1$ has no solution in natural numbers $x,y$ for which $q$ is a prime $> 3$.
References
    Chao Ko, Acta Sci. Natur. Univ. Szechuan. 2 (1960), 57-64.
  • Chao Ko, On the Diophantine equation $x^{2}=y^{n}+1,\,xy\not =0$, Sci. Sinica 14 (1965), 457–460. MR 183684
  • T. Nagell, Sur l’impossibilité de l’equation indéterminée ${y^2} = {z^p} + 1$, Norsk. Mat. Forenings Skrifter I 4 (1921).
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 56 (1976), 83-84
  • MSC: Primary 10B15
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0404133-1
  • MathSciNet review: 0404133