MathDB

N3

Part of 2017-IMOC

Problems(1)

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

8/14/2021
Find all functions f:N→N0f:\mathbb N\to\mathbb N_0 such that for all m,n∈Nm,n\in\mathbb N, \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*}
number theoryalgebrafefunctional equation