SOME EXPONENTIAL DIOPHANTINE EQUATIONS II: THE EQUATION x2 - Dy2 = kz FOR EVEN k

Let D be a nonsquare integer, and let k be an integer with vertical bar k vertical bar >= 1 and gcd(D, k) = 1. In the part I of this paper, using some properties on the representation of integers by binary quadratic primitive forms with discriminant 4D, M.-H. Le gave a series of explicit formulas for the integer solutions (x,y,z) of the equation x(2) - Dy-2 = k(z), gcd(x,y) = 1, z > 0 for 2 inverted iota vertical bar k vertical bar or is a power of 2. In this part, we give similar results for the other cases of k. (C) 2022 Mathematical Institute Slovak Academy of Sciences