Competition problem — Number theory

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Number theory Difficulty 5.8 AIME, harder Prove it

17. Show that if $p$ is prime and $1 \leqslant k<p$ , then the binomial coefficient $\binom{p}{k}$ is divisible by $p$ .

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.