# Modular Arithmetic/Wolstenholme's Theorem

 Modular Arithmetic ← Chinese Remainder Theorem Wolstenholme's Theorem Problem Set 1 →
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.
${\displaystyle \left({\begin{matrix}n\\k\end{matrix}}\right)}$ denotes the binomial coefficient, equal to ${\displaystyle {\frac {n!}{k!(n-k)!}}}$