Prime-row binomial coefficient divisibility
= Prime-row binomial coefficient divisibility
{title2=$p\mid\binom pr\quad(0<r<p)$}
For a <prime number> $p$, the identity $r!\binom pr=p(p-1)\cdots(p-r+1)$ has right side divisible by $p$, while $r!$ is coprime to $p$. Cancellation in <modular arithmetic> proves the divisibility.
// Target: combinatorics.bigb