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d - k and d are divisors of n

Source: 2018 Grand Duchy of Lithuania, Mathematical Contest p4 (Baltic Way TST)

October 3, 2020
number theorydividesdivisor

Problem Statement

Find all positive integers nn for which there exists a positive integer kk such that for every positive divisor dd of nn, the number dāˆ’kd - k is also a (not necessarily positive) divisor of nn.
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