kts1230
Oct14-11, 03:39 PM
1. The problem statement, all variables and given/known data
Suppose n and k are two positive integers, and they are relatively prime. Prove that n divides C(n,k) evenly. Then, give an example to show that this fact is not always true if n and k are not relatively prime.
2. Relevant equations
3. The attempt at a solution
I'm really struggling with this one but im almost positive that it has something to do with the fact that k*C(n,k) = n*C(n-1,k-1)
Suppose n and k are two positive integers, and they are relatively prime. Prove that n divides C(n,k) evenly. Then, give an example to show that this fact is not always true if n and k are not relatively prime.
2. Relevant equations
3. The attempt at a solution
I'm really struggling with this one but im almost positive that it has something to do with the fact that k*C(n,k) = n*C(n-1,k-1)