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

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.