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sum of divisors is a power of 2

Source: ICMC 2021 Round 1 P5

March 1, 2022

number theoryPowers of 2elementary-number-theoryICMCcollege contests

Problem Statement

Find all composite positive integers

m

such that, whenever the product of two positive integers

a

and

b

m

, their sum is a power of

2

.
Proposed by Harun Khan