Modular Arithmetic/Wolstenholme's Theorem

Wolstenholme's Theorem

For all prime numbers, $p>3$, the congruence,

$\left({\begin{matrix}2p-1\\p-1\end{matrix}}\right)\equiv 1{\pmod {p^{3}}}$

holds.

Where $\left({\begin{matrix}n\\k\end{matrix}}\right)$ denotes the binomial coefficient, which equals $n! \over k!(n-k)!$.