Maths question

Using the binomial theorem (see for example: http://en.wikipedia.org/wiki/Binomial_theorem)

(a+b)^p
=sum((p,k)a^(p-k)b^k) over k
where
(p,k)=p!/(k!(p-k)!)
if p is prime, then mod(p,k)=0 except k=0 and k=p where (p,k)=1.
Thus the summation simplifies to
(a+b)^p mod(p) = (a^p+b^p) mod(p)