Explain what is meant by an Euler pseudoprime and a strong pseudoprime. Show that 65 is an Euler pseudoprime to the base $b$ if and only if $b^{2} \equiv \pm 1(\bmod 65)$. How many such bases are there? Show that the bases for which 65 is a strong pseudoprime do not form a subgroup of $(\mathbb{Z} / 65 \mathbb{Z})^{\times}$.