olymmath

EGMO 2014 Problem 4

  • Day 2
  • Answer

Determine all 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+j2 i+j, then xi<xjx_{i}<x_{j}.

Proposed by Merlijn Staps, NLD The answer is that n=2kn=2^{k} with k≥1k \geq 1 or n=3⋅2kn=3 \cdot 2^{k} where k≥0k \geq 0.

Dataset text NuminaMath olympiads. Quoted with source.

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n=2^{k} \text{ with } k \geq 1 \text{ or } n=3 \cdot 2^{k} \text{ where } k \geq 0

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