Problem

Source: Iranian TST 2021, second exam day 2, problem 1

Tags: algebra, inequalities, function, number theory



Find all functions $f : \mathbb{N} \rightarrow \mathbb{R}$ such that for all triples $a,b,c$ of positive integers the following holds : $$f(ac)+f(bc)-f(c)f(ab) \ge 1$$ Proposed by Mojtaba Zare