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Math Help - exponent of a prime number in a factorial..!!

  1. #1
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    exponent of a prime number in a factorial..!!

    I was trying to deduct the logic of computing the exponent of a prime number p in n!, I could not get the logic at the first place, and then when I tried to go through some books, they referred to [n] where the [ ] denotes greatest integer <= n.

    Any help or explanation in this matter.


    DOTMATRIX
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by dotmatrix View Post
    I was trying to deduct the logic of computing the exponent of a prime number p in n!, I could not get the logic at the first place, and then when I tried to go through some books, they referred to [n] where the [ ] denotes greatest integer <= n.

    Any help or explanation in this matter.


    DOTMATRIX
    I assume you're talking about the fact that if ^k\mid n\}" alt="\eta(n,p)=\max\{k^k\mid n\}" /> then \displaystyle \eta(n,p)=\sum_{k=1}^{\infty}\left\lfloor\frac{n}{  p^k}\right\rfloor?
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  3. #3
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    [duplicate]

    For a prime p, in n!,
    each number 1 < kp \leq n contributes 1 to the exponent,
    and each number 1 < kp^2 \leq n contributes another 1 to the exponent,
    and each number 1 < kp^3 \leq n contributes another 1 to the exponent,
    ...

    From this, exponent of p in n! :
    \displaystyle \sum_{m=1}^\infty \lfloor \frac{n}{p^m} \rfloor
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  4. #4
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    got it bro..thanx a lot.
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