Sorry. I don't know why I put the "at most" in there. I want to prove that two primes ##p, q## exist that can divide ##\binom{n}{k}##. Sometimes only 1 prime is needed (i.e. when ##n## is prime). However, I want to prove that with only two primes, I can divide ##\binom{n}{k}##.
Also, each ##n##...
Homework Statement
Is it true that for each ##n\geq 2## there are two primes ##p, q \neq 1## that divide every ##\binom{n}{k}## for ##1\leq k\leq n-1##?Examples:
For ##n=6: \binom{6}{1}=6; \binom{6}{2}=15; \binom{6}{3}=20; \binom{6}{4}=15; \binom{6}{5}=6.## So we can have ##p=2## and...