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n/ 1^5 +3^5 +5^5 +...+(2n-1)^5, n^2 / 1^3 +3^3 +5^3 +...+(2n-1)^3

Source: Norwegian Mathematical Olympiad 1998 - Abel Competition p3

February 11, 2020
Sumnumber theorySum of powers

Problem Statement

Let nn be a positive integer. (a) Prove that 15+35+55+...+(2n−1)51^5 +3^5 +5^5 +...+(2n-1)^5 is divisible by nn. (b) Prove that 13+33+53+...+(2n−1)31^3 +3^3 +5^3 +...+(2n-1)^3 is divisible by n2n^2.
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