Gruppo delle terne quasi pitagoriche primitive

Abstract

We study the groupGm of primitive solution of the diophantine equationx2+my2=z2 (m>1, squarefree). Form∈3 this group is torsion free, form=3 it has a torsion element of order 3; moreover for a finite number of values ofm we prove thatGm is a direct sum of infinite cyclic groups and we give the generators ofGm in terms of the primes represented by the quadratic forms of discriminant Δ=−4m.