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


Author: E. Z. Chein
Journal: Proc. Amer. Math. Soc. 56 (1976), 83-84
MSC: Primary 10B15
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?)

  • [1] Chao Ko, Acta Sci. Natur. Univ. Szechuan. 2 (1960), 57-64.
  • [2] Chao Ko, On the Diophantine equation 𝑥²=𝑦ⁿ+1,𝑥𝑦̸=0, Sci. Sinica 14 (1965), 457–460. MR 0183684
  • [3] 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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DOI: https://doi.org/10.1090/S0002-9939-1976-0404133-1
Article copyright: © Copyright 1976 American Mathematical Society