$p^3\mid \binom{ap}{bp}-\binom{a}{b}$
$p^3\mid \binom{ap}{bp}-\binom{a}{b}$
Dato un primo $p\ge 5$ e interi positivi $a,b$, mostrare che $p^3$ divide $\binom{ap}{bp}-\binom{a}{b}$.
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