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Japan MO Finals 2021 P1

Source: Japan MO Finals 2021 P1

February 14, 2021
Japanfunctional equationnumber theory

Problem Statement

Find all functions from positive integers to themselves, such that for any positive integers m,nm,n the two conditions below are equivalent:
[*] nn divides mm. [*] f(n)f(n) divides f(m)āˆ’nf(m)-n.
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