Question 3
Let $k\ge14$ be an integer, and let $p_k$ be the largest prime number which is strictly less than $k$. You may assume that $p_k\ge3k/4$. Let $n$ be a composite integer. Prove:
(a) if $n=2p_k$, then $n$ does not divide $(n-k)!$;
(b) if $n\gt 2p_k$, then $n$ divides $(n-k)!$.
(a) if $n=2p_k$, then $n$ does not divide $(n-k)!$;
(b) if $n\gt 2p_k$, then $n$ divides $(n-k)!$.