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.

\left({\begin{matrix}n\\k\end{matrix}}\right)

denotes the binomial coefficient, equal to

{\frac {n!}{k!(n-k)!}}

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