On the solvability of the Diophantine equation dV ² − 2eV W − dW² = 1

Kenneth Hardy and Kenneth S. Williams

Vol. 124 (1986), No. 1, 145–158

DOI: 10.2140/pjm.1986.124.145

Abstract

This paper treats the diophantine equation dV ² − 2eV W − dW² = 1, where d and e are positive integers, by methods using the arithmetic of the ring of the gaussian integers.

Mathematical Subject Classification 2000

Primary: 11D09

Milestones

Received: 21 April 1985

Revised: 19 August 1985

Published: 1 September 1986