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Math Help - compostive

  1. #1
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    compostive

    n!+1 is composite.
    Last edited by rmpatel5; September 23rd 2008 at 07:21 PM.
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  2. #2
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    Hint given by book: use Wilson's theorem to guarantee that n!+1 has a prime factor for an appropriately chosen n
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  3. #3
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    Let n=p-1 then n! + 1 = (p-1)! + 1 \equiv 0 (\bmod p).
    Thus, p is a prime divisor.
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  4. #4
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    Quote Originally Posted by ThePerfectHacker View Post
    Let n=p-1 then n! + 1 = (p-1)! + 1 \equiv 0 (\bmod p).
    Thus, p is a prime divisor.
    would n! -1 be the same thing setting n=p-1 and getting (p-1)!-1 but since 1 is the only inverse modulo of itself it is the same thing as (p-1)!+1??
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