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Math Help - Fermat's Little Theorem

  1. #1
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    Fermat's Little Theorem

    Let p be a prime number, not 2 or 5.

    Show that 10^{p-1} \equiv 1 \pmod p \quad \quad

    I can show the workings for some primes i.e 3,7 but how do i show for all primes except 2 and 5?

    thanks
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by charikaar View Post
    Let p be a prime number, not 2 or 5.

    Show that 10^{p-1} \equiv 1 \pmod p \quad \quad

    I can show the workings for some primes i.e 3,7 but how do i show for all primes except 2 and 5?

    thanks
    Let p be a prime, then \left(10,p\right)\ne1 if and only if p=2,5 (this is easy to deduce). So...apply the name of this thread.
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