Problem

Source: Iran TST 2023 ; Exam 1 Problem 5

Tags: function, algebra



Suppose that n2 and a1,a2,...,an are natural numbers that (a1,a2,...,an)=1. Find all strictly increasing function f:ZR that: x1,x2,...,xnZ:f(ni=1xiai)=ni=1f(xiai) Proposed by Navid Safaei and Ali Mirzaei