DE-MO 2002 Problem 3

Prove that for all primes $p$ true is equality $\sum_{k=1}^{p-1}\left\lfloor\frac{k^3}{p}\right\rfloor=\frac{(p-2)(p-1)(p+1)}{4}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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