f(mn)=f(m)f(n) and f(m+n)=min(f(m),f(n)) if f(m)≠f(n) over N->N0
Source: IMOC 2017 N3
August 14, 2021
number theoryalgebrafefunctional equation
Problem Statement
Find all functions such that for all ,
\begin{align*}
f(mn)&=f(m)f(n)\\
f(m+n)&=\min(f(m),f(n))\qquad\text{if }f(m)\ne f(n)\end{align*}