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a^2_n$ divides a_{n-1}a_{n+1}

Source: 2015 Saudi Arabia Pre-TST 3.3

September 12, 2020
number theorydivides

Problem Statement

Let (an)n≥0(a_n)_{n\ge0} be a sequence of positive integers such that an2a^2_n divides an−1an+1a_{n-1}a_{n+1}, for all n≥1n \ge 1. Prove that if there exists an integer k≥2k \ge 2 such that aka_k and a1a_1 are relatively prime, then a1a_1 divides a0a_0.
(Malik Talbi)
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