Minimal Solutions of Diophantine Equations

Abstract

Our aim is to prove: If a, b, c are positive integers, if ab > 1, if a, b, c are relatively prime in pairs, and all are free of squares, if — ab is a quadratic residue of c, bc of a, ca of b, and if F(x, y, z) = ax 2 + by 2 — cz 2 , we have non-trivial solutions of with the inequalities