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n divides 2i+j determines a sequence

Source: European Girls’ Mathematical Olympiad 2014 - Day 2 - P4

April 13, 2014
modular arithmeticnumber theoryEGMOEGMO 2014Divisibility

Problem Statement

Determine all positive integers n≥2n\geq 2 for which there exist integers x1,x2,…,xn−1x_1,x_2,\ldots ,x_{n-1} satisfying the condition that if 0<i<n,0<j<n,i≠j0<i<n,0<j<n, i\neq j and nn divides 2i+j2i+j, then xi<xjx_i<x_j.
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