International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 35, Pages 2241-2253
doi:10.1155/S0161171203204348

The Diophantine equation ax2+2bxy−4ay2=±1

Lionel Bapoungué

 Département de Mathématiques, École Normale Supérieure, Université de Yaoundé 1, Yaoundé BP 47, Cameroon
Received 30 April 2002

Abstract

We discuss, with the aid of arithmetical properties of the ring of the Gaussian integers, the solvability of the Diophantine equation ax2+2bxy−4ay2=±1, where a and b are nonnegative integers. The discussion is relative to the solution of Pell's equation v2−(4a2+b2)w2=−4.