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Relatively prime to all the terms

Source: 2016 Greece,Team Selection Test,Problem 1

July 8, 2016
number theorySequenceDivisibility

Problem Statement

Given is the sequence (an)n≥0(a_n)_{n\geq 0} which is defined as follows:a0=3a_0=3 and an+1−an=n(an−1) , ∀n≥0a_{n+1}-a_n=n(a_n-1) \ , \ \forall n\geq 0.
Determine all positive integers mm such that gcd⁡(m,an)=1 , ∀n≥0\gcd (m,a_n)=1 \ , \ \forall n\geq 0.
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