Sum of odd powers

Algebra Level 4

For positive integer \(n\), let \(f(n) \) denote the remainder when \(\displaystyle 3\sum_{r=1}^n r^5 \) is divided by \( \displaystyle \sum_{r=1}^n r^3 \). Compute \( f(1) + f(2) + \cdots +f (2016 ) \).

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