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minimum of two consecutive terms is less than 1

Source: 2023 Thailand Online MO P7

February 12, 2023
Inequalityalgebra

Problem Statement

Let a0,a1,…a_0,a_1,\dots be a sequence of positive reals such that an+2≤2023ananan+1+2023 a_{n+2} \leq \frac{2023a_n}{a_na_{n+1}+2023} for all integers n≥0n\geq 0. Prove that either a2023<1a_{2023}<1 or a2024<1a_{2024}<1.
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