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Sad Combinatorics II

Source: 2018 USAMO 6, by Richard Stong

April 19, 2018
USAMO2018 USAMO Problem 6

Problem Statement

Let ana_n be the number of permutations (x1,x2,…,xn)(x_1, x_2, \dots, x_n) of the numbers (1,2,…,n)(1,2,\dots, n) such that the nn ratios xkk\frac{x_k}{k} for 1≤k≤n1\le k\le n are all distinct. Prove that ana_n is odd for all n≥1n\ge 1.
Proposed by Richard Stong
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