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International Journal of Mathematics and Mathematical Sciences - Volume 25 2001, Issue 5, Pages 289-292

Department of Mathematics, University of California at Berkeley, Berkeley 94709, CA, USA

Received 26 February 1998; Revised 17 May 2000

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper proves that if N is a nonnegative eligible integer,coprime to 7, which is not of the form x2+y2+7z2, then N is square-free. The proof is modelled on that of a similartheorem by Ono and Soundararajan, in which relations between thenumber of representations of an integer np2 by two quadraticforms in the same genus, the pth coefficient of an L-functionof a suitable elliptic curve, and the class number formula provethe theorem for large primes, leaving 3 cases which are easilynumerically verified.





Autor: James Kelley

Fuente: https://www.hindawi.com/



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