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4

Part of 2021 Benelux

Problems(1)

Sequence not containing a multiple of p (BxMO2021 P4)

Source: BxMO2021 problem 4

5/3/2021
A sequence a1,a2,a3,…a_1, a_2, a_3, \ldots of positive integers satisfies a1>5a_1 > 5 and an+1=5+6+⋯+ana_{n+1} = 5 + 6 + \cdots + a_n for all positive integers nn. Determine all prime numbers pp such that, regardless of the value of a1a_1, this sequence must contain a multiple of pp.
BxMOnumber theory