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non-trivial divisors add up to n-1

Source: Own. IMO 2021 Malaysian Training Camp 1

December 31, 2020
number theoryDivisorsPerfect Numbers

Problem Statement

Given a natural number nn, call a divisor dd of nn to be <spanclass=′latex−italic′>nontrivial</span><span class='latex-italic'>nontrivial</span> if d>1d>1. A natural number nn is <spanclass=′latex−italic′>good</span><span class='latex-italic'>good</span> if one or more distinct nontrivial divisors of nn sum up to n−1n-1.
Prove that every natural number nn has a multiple that is good.
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