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Spanish Mathematical Olympiad 2016 Day 2 Problem 5

Source:

April 4, 2016
combinatoricspermutationsPermutations with restrictionsSetsnational olympiadOlympiad

Problem Statement

From all possible permutations from (a1,a2,...,an)(a_1,a_2,...,a_n) from the set {1,2,..,n}\{1,2,..,n\}, n≥1n\geq 1, consider the sets that satisfies the 2(a1+a2+...+am)2(a_1+a_2+...+a_m) is divisible by mm, for every m=1,2,...,nm=1,2,...,n. Find the total number of permutations.
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