# Math Help - Prove

1. ## Prove

If p is prime, prove that (a+b)^p is congruent to a^p + b^p (mod p)

2. Originally Posted by mandy123
If p is prime, prove that (a+b)^p is congruent to a^p + b^p (mod p)
If you expand (a+b)^p as a binomial the intermediatary terms ${p\choose k}a^pb^{p-k}$ for $1\leq k\leq p-1$ become that $p$ divides ${p\choose k}$.