MathDB

N6

Part of 2021 IMO Shortlist

Problems(1)

Divisibility rearrangement

Source: 2021 ISL N6

7/12/2022
Determine all integers n⩾2n\geqslant 2 with the following property: every nn pairwise distinct integers whose sum is not divisible by nn can be arranged in some order a1,a2,…,ana_1,a_2,\ldots, a_n so that nn divides 1⋅a1+2⋅a2+⋯+n⋅an.1\cdot a_1+2\cdot a_2+\cdots+n\cdot a_n.
Arsenii Nikolaiev, Anton Trygub, Oleksii Masalitin, and Fedir Yudin
number theoryIMO ShortlistAZE IMO TST