Criteria for Simultaneous Solutions of X2 − DY2 = c and x2 − Dy2 = −c

Abstract

AbstractThe purpose of this article is to provide criteria for the simultaneous solvability of the Diophantine equations X2 − DY2 = c and x2 − Dy2 = −c when c ∊ ℤ, and D ∊ ℕ is not a perfect square. This continues work in [6]–[8].