  Equivalence classes of solutions of the Diophantine equation $a^2+mb^2=c^2$
form an infinitely generated abelian group $G_m$, where $m$ is a fixed
square-free positive integer. Solutions of Pell's equation $x^2-my^2=1$
generate a subgroup $P_m$ of $G_m$. We prove that $P_m$ and $G_m/P_m$ have
infinite rank for all $m>1$. We also give several examples of $m$ for which
$G_m/P_m$ has nontrivial torsion.
