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Find n integers such that a_i divides a_j^2+1 for any i,j

Source: Francophone 2024, Junior P4

April 4, 2024
number theorynumber theory proposedDivisibilitySequence

Problem Statement

Find all integers n≥2n \ge 2 for which there exists nn integers a1,a2,…,an≥2a_1,a_2,\dots,a_n \ge 2 such that for all indices i≠ji \ne j, we have ai∣aj2+1a_i \mid a_j^2+1.
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