On the subgroup generated by solutions of Pell's equation

Equivalence classes of solutions of the Diophantine equation a2+mb2=c2 form an infinitely generated abelian group Gm, where m is a fixed square-free positive integer. Solutions of Pell's equation x2−my2=1 generate a subgroup Pm of Gm. We prove that Pm and Gm/Pm have infinite rank for all m>1. We also give several examples of m for which Gm/Pm has nontrivial torsion.