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Floor double summation

Source: ISL 2021 A2

July 12, 2022
algebrafloor functionIMO ShortlistISL 2021SummationNumberTheory

Problem Statement

Which positive integers nn make the equation ∑i=1n∑j=1n⌊ijn+1⌋=n2(n−1)4\sum_{i=1}^n \sum_{j=1}^n \left\lfloor \frac{ij}{n+1} \right\rfloor=\frac{n^2(n-1)}{4} true?
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