Solution
= Solution
$N$ is a <Fermat pseudoprime> to base $b$ when it is composite, coprime to $b$, and $b^{N-1}\equiv1\pmod N$. Here $N\mid b^k-1$ gives coprimality and $k\mid N-1$, so $b^{N-1}=(b^k)^{(N-1)/k}\equiv1\pmod N$.
= Solution
$N$ is a <Fermat pseudoprime> to base $b$ when it is composite, coprime to $b$, and $b^{N-1}\equiv1\pmod N$. Here $N\mid b^k-1$ gives coprimality and $k\mid N-1$, so $b^{N-1}=(b^k)^{(N-1)/k}\equiv1\pmod N$.