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a_{n+1} - a_n = n(a_n - 1)

Source: 2021 Dutch IMO TST 1.1

December 28, 2021
number theorySequencerecurrence relation

Problem Statement

The sequence of positive integers a0,a1,a2,...a_0, a_1, a_2, . . . is defined by a0=3a_0 = 3 and an+1−an=n(an−1)a_{n+1} - a_n = n(a_n - 1) for all n≥0n \ge 0. Determine all integers m≥2m \ge 2 for which gcd(m,an)=1gcd (m, a_n) = 1 for all n≥0n \ge 0.
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