Sunday, 15 December 2013

number theory - How to find the exponent of a prime in n!

Let the positive integer n be written as powers of prime p so that we have n=akpk+....+a2p2+a1p+a0, where $0\leq a_i
n(ak+....+a1+a0)p1.



I know that the exponent of p in n! is k=1npk. But I got stuck on how to use the given expression of n. Any suggestions?

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