MathDB
Fractions, prime, floor, sum

Source: 41 German Math Olympiad, Bundesrunde, Grade 13, P3

June 20, 2019
number theory

Problem Statement

Prove that for all primes pp true is equality ∑k=1p−1⌊k3p⌋=(p−2)(p−1)(p+1)4\sum_{k=1}^{p-1}\left\lfloor\frac{k^3}{p}\right\rfloor=\frac{(p-2)(p-1)(p+1)}{4}
Back to ProblemsView on AoPS