Let k≥14 be an integer, and let pk be the largest prime number which is strictly less than k. You may assume that pk≥3k/4. Let n be a composite integer. Prove:
(a) if n=2pk, then n does not divide (n−k)!;
(b) if n>2pk, then n divides (n−k)!. number theoryprime numbersAPMO