First sorry about plain ASCII (LaTeX isn't working atm :/). The task is to prove following theorem: if 1<k<p is prime factor of p, then C(p, k) isn't divisible by p.
I think I have seen a proof, which states that: If p is a prime and 0<r<p, then C(p, r) is divisible by p. But, I don't remeber, how that was proven.
So, any help is appreciated. Thanks in advance!