Exercise 2.7.8 (The proof of Wolstenholme's congruence fails when $p=3$)

Proof. The last argument of the proof is ${\sigma }_{p-3}\equiv 0(\mathit{mod}p)$. But if $p=3$, ${\sigma }_0$ is not defined.

(If we define ${\sigma }_i$ for $0\le i\le p-1$ by

then ${\sigma }_0=1$.) □