Question 71
Denote by $\mathbb{Q}^{+}$ the set of positive rational numbers. A function $f: \mathbb{Q}^{+} \rightarrow \mathbb{Q}$ satisfies
- $f(p)=1$ for all primes $p$, and
- $f(a b)=a f(b)+b f(a)$ for all $a, b \in \mathbb{Q}^{+}$.
For which positive integers $n$ does the equation $n f(c)=c$ have at least one solution $c$ in $\mathbb{Q}^{+}$?
- $f(p)=1$ for all primes $p$, and
- $f(a b)=a f(b)+b f(a)$ for all $a, b \in \mathbb{Q}^{+}$.
For which positive integers $n$ does the equation $n f(c)=c$ have at least one solution $c$ in $\mathbb{Q}^{+}$?