Question 17
For each integer $n$ ($n \ge 2$) let $f(n)$ denote the sum of all positive integers that are at most $n$ and not relatively prime to $n$.
Prove that $f(n+p) \neq f(n)$ for each such $n$ and for every prime $p$.
Prove that $f(n+p) \neq f(n)$ for each such $n$ and for every prime $p$.