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Sequence not containing a multiple of p (BxMO2021 P4)

Source: BxMO2021 problem 4

May 3, 2021

BxMOnumber theory

Problem Statement

A sequence

a_1, a_2, a_3, \ldots

of positive integers satisfies

a_1 > 5

and

a_{n+1} = 5 + 6 + \cdots + a_n

for all positive integers

n

. Determine all prime numbers

p

such that, regardless of the value of

a_1

, this sequence must contain a multiple of

p