Let $N \geqslant 3$ be an odd integer and $b$ an integer with $(b, N)=1$. What does it mean to say that $N$ is an Euler pseudoprime to base $b$ ?

Show that if $N$ is not an Euler pseudoprime to some base $b_{0}$, then it is not an Euler pseudoprime to at least half the bases $\{1 \leqslant b<N:(b, N)=1\}$.

Show that if $N$ is odd and composite, then there exists an integer $b$ such that $N$ is not an Euler pseudoprime to base $b$.