Frankin 5.P.

Let $p$ be a prime number. How many natural numbers $n$ exist such that $p n$ is divisible by $p+n$?
Let $p n=(p+n) k$, then $p^{2}=p^{2}+p n-(p+n) k=(p+n)(p-k)$. Since $p-k<p$, it does not divide $p$.

Therefore, $p+n=p^{2}$, that is, $n=p^{2}-p$. Obviously, it fits.

## Answer

One.