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Proceedings of the American Mathematical Society

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The Diophantine equation $x^p+1=py^2$


Author: J. H. E. Cohn
Journal: Proc. Amer. Math. Soc. 131 (2003), 13-15
MSC (2000): Primary 11D61
DOI: https://doi.org/10.1090/S0002-9939-02-06732-1
Published electronically: August 19, 2002
MathSciNet review: 1929016
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Abstract: Cao has recently proved that, subject to a certain condition on the odd prime $p$, the equation $x^p+1=py^2$ has no solutions in positive integers $x$ and $y$, provided also that $p\equiv1\pmod 4$. It is the object of this note to remove this restriction, and to provide a simple self-contained proof.


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Additional Information

J. H. E. Cohn
Affiliation: Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom
Email: j.cohn@rhul.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-02-06732-1
Received by editor(s): July 13, 2001
Published electronically: August 19, 2002
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2002 American Mathematical Society