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2011 ToT Fall Junior A p1 sequence of positive integers, divisors related

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March 22, 2020
divisornumber theory

Problem Statement

An integer N>1N > 1 is written on the board. Alex writes a sequence of positive integers, obtaining new integers in the following manner: he takes any divisor greater than 11 of the last number and either adds it to, or subtracts it from the number itself. Is it always (for all N>1N > 1) possible for Alex to write the number 20112011 at some point?