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Math Help - Pairwise distinct primes

  1. #1
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    Pairwise distinct primes

    Let n = p1.....pm for pairwise distinct primes pi other than 2 and 5. Let ki
    be the period of the decimal expression of 1/pi. Show that the period of the decimal
    expression of 1/n is the least common multiple of k1,....,km.
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  2. #2
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    Re: Pairwise distinct primes

    Hi,
    The attachment should enable you to give a proof:

    Pairwise distinct primes-mhfnumbertheory3.png
    Thanks from emakarov and yipying
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  3. #3
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    Re: Pairwise distinct primes

    A proof of the first fact can be found in Elementary Number Theory by Dudley, which is available online.

    Section 15, p. 118, Theorem 4. If (n, 10) = 1, then the period of 1/n is the order of 10 modulo n.
    Thanks from yipying
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