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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 35, Pages 2241-2253
http://dx.doi.org/10.1155/S0161171203204348

The Diophantine equation ax2+2bxy4ay2=±1

Département de Mathématiques, École Normale Supérieure, Université de Yaoundé 1, Yaoundé BP 47, Cameroon

Received 30 April 2002

Copyright © 2003 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

We discuss, with the aid of arithmetical properties of the ring of the Gaussian integers, the solvability of the Diophantine equation ax2+2bxy4ay2=±1, where a and b are nonnegative integers. The discussion is relative to the solution of Pell's equation v2(4a2+b2)w2=4.