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How to make weird functions be like:

Source: Bolivia Ibero TST 2021 Day 1 P2

September 2, 2022
functionnumber theoryBoliviaTSTfunctional equation

Problem Statement

Let f:Z+→Zf: \mathbb Z^+ \to \mathbb Z be a function such that a) f(p)=1f(p)=1 for every prime pp. b) f(xy)=xf(y)+yf(x)f(xy)=xf(y)+yf(x) for every pair of positive integers x,yx,y Find the least number n≥2021n \ge 2021 such that f(n)=nf(n)=n
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