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Infinite sequence of positive integers (2015 OMCS #5)

Source:

May 16, 2015

number theoryDivisibilitySequence

Problem Statement

Determine if there exists an infinite sequence of not necessarily distinct positive integers

a_1, a_2, a_3,\ldots

such that for any positive integers

m

and

n

where

1 \leq m < n

, the number

a_{m+1} + a_{m+2} + \ldots + a_{n}

is not divisible by

a_1 + a_2 + \ldots + a_m