Siberian Federal University

Let a; b and c be positive integers such that a2+b2 = c2 with gcd (a; b; c) = 1, a even. Terai’s conjecture claims that the Diophantine equation x2 + by = cz has only the positive integer solution (x; y; z) = (a; 2; 2). In this short note, we prove that the equation of the title, has only the positive integer solution (u; v;w) = (2; 2; 4q + 1); where q is a positive integer