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A note on the equation $x^{2}=y^{q}+1$


Author: E. Z. Chein
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
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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 [Enhancements On Off] (What's this?)

    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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Article copyright: © Copyright 1976 American Mathematical Society