Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

The Diophantine equation

Author(s): J. H. E. Cohn
Journal: Proc. Amer. Math. Soc. 131 (2003), 13-15.
MSC (2000): Primary 11D61
Posted: August 19, 2002
MathSciNet review: 1929016
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Abstract | References | Similar articles | Additional information

Abstract: Cao has recently proved that, subject to a certain condition on the odd prime , the equation has no solutions in positive integers and , 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.

References:

1.: Z. Cao, On the Diophantine equation $x^p+2^{2m}=py^2$ , Proc. Amer. Math. Soc. 128 (2000), 1927-1931. MR 2000m:11028
2.: A. J. van Poorten, H. J. te Riele and H. C. Williams, Computer verification of the Ankeny-Artin-Chowla conjecture for all primes less than $100{\phantom{X}}000{\phantom{X}}000{\phantom{X}}000$ , Math. Comp. 70 (2001), 1311-1328. MR 2001j:11125

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