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## Functional equation on positive integers

Let be a fixed positive integer. Find all functions such that we have .

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**Answer: ** for every .

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Categories: Uncategorized
functional equation

What is ?

is a positive integer.

Is it fixed or for arbitrary ? How about ?

Yes, it is the same for all . The particular case was given to an old IMO; I do not know exactly the year. I’ll edit the post of the problem, so that there is no confusion. And I’ll add a solution if you want.