The Diophantine equation $x^p+1=py^2$
HTML articles powered by AMS MathViewer
- by J. H. E. Cohn PDF
- Proc. Amer. Math. Soc. 131 (2003), 13-15 Request permission
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 $p\equiv 1\pmod 4$. It is the object of this note to remove this restriction, and to provide a simple self-contained proof.References
- Zhenfu Cao, On the Diophantine equation $x^p+2^{2m}=py^2$, Proc. Amer. Math. Soc. 128 (2000), no. 7, 1927–1931. MR 1694856, DOI 10.1090/S0002-9939-00-05517-9
- A. J. van der Poorten, H. J. J. te Riele, and H. C. Williams, Computer verification of the Ankeny-Artin-Chowla conjecture for all primes less than $100\,000\,000\,000$, Math. Comp. 70 (2001), no. 235, 1311–1328. MR 1709160, DOI 10.1090/S0025-5718-00-01234-5
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
- Received by editor(s): July 13, 2001
- Published electronically: August 19, 2002
- Communicated by: David E. Rohrlich
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 13-15
- MSC (2000): Primary 11D61
- DOI: https://doi.org/10.1090/S0002-9939-02-06732-1
- MathSciNet review: 1929016