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Grade 9, great divisor

Source: AllRussian-2014, Grade 9, day2, P1

May 3, 2014
number theory proposednumber theory

Problem Statement

Define m(n)m(n) to be the greatest proper natural divisor of n∈Nn\in \mathbb{N}. Find all n∈Nn \in \mathbb{N} such that n+m(n)n+m(n) is a power of 1010.
N. Agakhanov
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