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Part of 2020 OMMock - Mexico National Olympiad Mock Exam

Problems(1)

At least 2020 permutations giving distinct remainder for some n

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

11/8/2020
We say that a permutation (a1,…,an)(a_1, \dots, a_n) of (1,2,…,n)(1, 2, \dots, n) is good if the sums a1+a2+⋯+aia_1 + a_2 + \dots + a_i are all distinct modulo nn. Prove that there exists a positive integer nn such that there are at least 20202020 good permutations of (1,2,…,n)(1, 2, \dots, n).
Proposed by Ariel García
number theorypermutationsremainder