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Sum of the numbers is divisible by k

Source: LXII Polish Olympiad 2011, Problem 1

May 24, 2011
number theory unsolvednumber theory

Problem Statement

Find all integers n≥1n\geq 1 such that there exists a permutation (a1,a2,...,an)(a_1,a_2,...,a_n) of (1,2,...,n)(1,2,...,n) such that a1+a2+...+aka_1+a_2+...+a_k is divisible by kk for k=1,2,...,nk=1,2,...,n
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