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#1

$Old$ November 2nd, 2009, 06:00 PM

steph3824 $steph3824 is offline$

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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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$Old$ November 2nd, 2009, 10:00 PM

tonio $tonio is online now$

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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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