Abstract :
Let D be a non-square integer, and let D1, D2 be integers satisfying D1D2 = D, D1 > 0 and gcd(D1, D2) = 1. Let k be an integer with k > 1 and gcd(D, k) = 1. In this paper we give some explicit formulas for all integer solutions (x, y, z) of the equation D1x2 −D2y2 = λkz, gcd(x, y) = 1, z > 0, where λ is equal to 1 or 4 according as 2 [formula]k or not.
