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Let http://www.cramster.com/Answer-Board...6185762832.gif with n>1, and let p be a prime number. If http://www.cramster.com/Answer-Board...7486624507.gifhttp://www.cramster.com/answer-board...b34e757044.jpg n!, prove that the exponent of p in the prime factorization of n! is [n/p] + [n/p^2] + [n/p^3] +......(Note that this sum is finite, since [n/p^m]=0 if p^m>n
Note that in the setQuote:
Originally Posted by rmpatel5
there are
multiples of
. But
of these, are multiple of
and so on.
You must count once the numbers which are multiples of p but not of p², twice the numbers which are multiple of p² and not of p³,... , in order to get the maximum power of p dividing n!
And to do so it's enough to sum
I am still lost in this proof.Quote:
Originally Posted by PaulRSNote that in the set
You must count once the numbers which are multiples of p but not of p², twice the numbers which are multiple of p² and not of p³,... , in order to get the maximum power of p dividing n!
And to do so it's enough to sum