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Math Help - Divisibility problem

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    Divisibility problem

    Let a+b=p, where a and b are positive integer numbers and p is a prime. Prove that a^p+b^p is divisible by p^2, but it is not divisible by p^3!
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by gabor7896 View Post
    Let a+b=p, where a and b are positive integer numbers and p is a prime. Prove that a^p+b^p is divisible by p^2, but it is not divisible by p^3!
    a^p+b^p=\left(a+b\right)^p-\sum_{k=1}^{p-1}{p \choose k}a^{p-k}b^k, start with that.
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