Problem

Source: Mexico National Olympiad Mock Exam (OMMock) 2020 P2

Tags: number theory, permutations, remainder



We say that a permutation $(a_1, \dots, a_n)$ of $(1, 2, \dots, n)$ is good if the sums $a_1 + a_2 + \dots + a_i$ are all distinct modulo $n$. Prove that there exists a positive integer $n$ such that there are at least $2020$ good permutations of $(1, 2, \dots, n)$. Proposed by Ariel GarcĂ­a