MathDB

A2

Part of 2021 IMO Shortlist

Problems(1)

Floor double summation

Source: ISL 2021 A2

7/12/2022
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?
algebrafloor functionIMO ShortlistISL 2021SummationNumberTheory