Question 31
Let $f$ be a function with the following properties:
1) $f(n)$ is defined for every positive integer $n$;
2) $f(n)$ is an integer;
3) $f(2)=2$;
4) $f(m n)=f(m) f(n)$ for all $m$ and $n$;
5) $f(m)\gt f(n)$ whenever $m\gt n$.
Prove that $f(n)=n$.
1) $f(n)$ is defined for every positive integer $n$;
2) $f(n)$ is an integer;
3) $f(2)=2$;
4) $f(m n)=f(m) f(n)$ for all $m$ and $n$;
5) $f(m)\gt f(n)$ whenever $m\gt n$.
Prove that $f(n)=n$.