# Thread: Prime factors and binomial coefficients

1. ## Prime factors and binomial coefficients

Hello,
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!

2. Originally Posted by Greg98
Hello,
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!
How rigorous do you want to be? Write out C(p,k) and note there is a factor of p in the numerator and since all the factors in the denominator are strictly less than p none of them can 'cancel' the p.