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Math Help - Immediate Consequences of Fermat's Little Theorem

  1. #1
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    Immediate Consequences of Fermat's Little Theorem

    Hi

    I'm a high school student, so pardon me for my innocence. I am doing prime number recognition for my extended essay. And could someone kindly explain the immediate consequence portion of Fermat's Little Theorem as posted here?

    The little book of big primes - Google Books

    Thanks.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Hello there,

    I would love to help you. But can you please say what, more specifically, you are having trouble with? I cannot paraphrase a whole section of the book...
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  3. #3
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    The portion that says:

    "Note the following immediate consequence (of the theorem): if p does not divide a and p^n is the highest power of p dividing a^(p-1), then p^(n+e) is the highest power dividing[ a^((p^e)(p-1)) - 1] where e is greater than or equal to 1; in this statement, if p = 2, then n must be at least 2."

    Thanks
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