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Infinitely many k such that f(k)=1

Source: CSMO 2019 Grade 10 Problem 3

July 30, 2019
functionnumber theory

Problem Statement

Let f:N→Nf:\mathbb{N}\rightarrow \mathbb{N} be a function such that f(ab)f(ab) divides max⁡{f(a),b}\max \{f(a),b\} for any positive integers a,ba,b. Must there exist infinitely many positive integers kk such that f(k)=1f(k)=1?
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