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Math Help - Need help with a proof involving congruence and mod stuff

  1. #1
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    Question Need help with a proof involving congruence and mod stuff

    Prove that if a and b are integers and p is a prime, then (a+b)^p is congruent to a^(p)+b^(p) (mod p). Help please?
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    Quote Originally Posted by steph3824 View Post
    Prove that if a and b are integers and p is a prime, then (a+b)^p is congruent to a^(p)+b^(p) (mod p). Help please?

    (a+b)^p=\sum\limits_{k=0}^p\binom{p}{k}a^{p-k}b^k.

    Well, now just prove that for  1\leq k\leq p-1\,,\,\,p\mid \binom{p}{k} and you're done

    Tonio
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