Suppose that $m$ is a square-free positive integer, $m \geqslant 5, m \not \equiv 1 \quad(\bmod 4)$. Show that, if the class number of $K=\mathbb{Q}(\sqrt{-m})$ is prime to 3 , then $x^{3}=y^{2}+m$ has at most two solutions in integers. Assume the $m$ is even.