Let be a prime number, and let m and be positive integers. Show that is divisible by p.

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- Aug 19th 2011, 11:35 PMalexmahoneBinomial coefficient
Let be a prime number, and let m and be positive integers. Show that is divisible by p.

- Aug 20th 2011, 02:35 PMmeleseRe: Binomial coefficient
We have the simple identity for . Hence,

*(a)*.

Let be the largest power of that divides . So , by*(a)*.

From it follows that and so divides , where does not divide . Euclid's Lemma implies then that must divide .

By the way, the argument works for also.