# Thread: Need help with a proof involving congruence and mod stuff

1. ## 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?

2. Originally Posted by steph3824
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