a) Suppose that n is an odd integer. Prove that k(n−k) is divisible by 2 for all positive integers k.b) Find an integer k such that k(100−k) is not divisible by 11.c) Suppose that p is an odd prime, and n is an integer.
Prove that there is an integer k such that k(n−k) is not divisible by p. d) Suppose that p,q are two different odd primes, and n is an integer.
Prove that there is an integer k such that k(n−k) is not divisible by any of p,q. number theoryoddprimesdividesdivisible