Modular Arithmetic/Wolstenholme's Theorem

For all prime numbers, ${\displaystyle p>3}$, the congruence,

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

holds.

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