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Math Help - Pseudoprimes #2

  1. #1
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    Post Pseudoprimes #2

    Let p be prime, prove that if (2^p)-1 is a composite number, then m=(2^p)-1 is a pseudoprime.
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  2. #2
    Junior Member
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    n = 2^p -1 == (denotes congruent)

    2^(p-1) == 1modp by fermats little theorem

    since p is an odd prime.

    p|(2^(p-1)-1)

    so p|n-1

    n = 2^p -1|2^(n-1) -1

    2^(n-1) == 1mod n

    and 2^n == 2 mod n, so n is a pseudoprime
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