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Math Help - Extremely difficult number theory problem?

  1. #1
    Super Member fardeen_gen's Avatar
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    Extremely difficult number theory problem?

    For a prime and a given integer let denote the exponent of in the prime factorisation of . Given and a set of primes, show that there are infinitely many positive integers such that for all .
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  2. #2
    Super Member fardeen_gen's Avatar
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    I had a go at this question again but it yielded no results. None of the general number theory related theorems helped ...
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  3. #3
    MHF Contributor
    Opalg's Avatar
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    I don't know if this helps at all, but apparently there is a formula due to Legendre saying that <br />
\nu_p(n!) = \frac{n-s_p(n)}{p-1}, where s_p(n) is the sum of the digits of n in base p.

    Reference: http://www.math.tulane.edu/~vhm/web_html/k-central.pdf (pdf file).
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