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2018 USAMO Problems/Problem 6

Revision as of 10:52, 21 April 2018 by Sujaykazi (talk | contribs) (Created page with "==Problem 6== Let <math>a_n</math> be the number of permutations <math>(x_1, x_2, \dots, x_n)</math> of the numbers <math>(1,2,\dots, n)</math> such that the <math>n</math> ra...")
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Problem 6

Let $a_n$ be the number of permutations $(x_1, x_2, \dots, x_n)$ of the numbers $(1,2,\dots, n)$ such that the $n$ ratios $\frac{x_k}{k}$ for $1\le k\le n$ are all distinct. Prove that $a_n$ is odd for all $n\ge 1.$


Solution

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