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Possible Duplicate:
Using Fermat’s Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +…+(p-1)^p \equiv 0 \bmod{p}$

If p is an odd prime, prove: (Using Fermat's Theorem, both versions)

a)$1^p + 2^p + 3^p +\cdots+(p-1)^p$ is congruent to $0\pmod p$

b) $1^{p-1} + 2^{p-1} + \cdots+(p-1)^{p-1}$ is congruent to $-1\pmod p$

I know both verisons are:

$q^p =q\pmod p$ and $q^{p-1}=1 \pmod p$

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    And http://math.stackexchange.com/questions/255843/using-fermats-little-theorem-prove-if-p-is-prime-prove-1p-1-2p-12012-12-12

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