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Sequence of biggest prime divisors

Source: 2018 Latvia BW TST P14

March 26, 2022
number theorynumber theory unsolvedInteger sequence

Problem Statement

Let a1,a2,...a_1,a_2,... be a sequence of positive integers with a1=2a_1=2. For each n≥1n \ge 1, an+1a_{n+1} is the biggest prime divisor of a1a2...an+1a_1a_2...a_n+1. Prove that the sequence does not contain numbers 55 and 1111.
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