NO-ABEL 1998 Problem 3

Let $n$ be a positive integer. (a) Prove that $1^5 +3^5 +5^5 +...+(2n-1)^5$ is divisible by $n$ . (b) Prove that $1^3 +3^3 +5^3 +...+(2n-1)^3$ is divisible by $n^2$ .