MathDB
Easy problem to give us comfort

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

May 22, 2021
algebrainequalitiesfunctionnumber theory

Problem Statement

Find all functions f:N→Rf : \mathbb{N} \rightarrow \mathbb{R} such that for all triples a,b,ca,b,c of positive integers the following holds :
f(ac)+f(bc)−f(c)f(ab)≥1f(ac)+f(bc)-f(c)f(ab) \ge 1
Proposed by Mojtaba Zare
Back to ProblemsView on AoPS