Question 29
Let $N$ be the set of positive integers. Let $f: \mathbb{N} \to \mathbb{N}$ be a function satisfying the following two conditions:
a. $f(m)$ and $f(n)$ are relatively prime whenever $m$ and $n$ are relatively prime.
b. $n \le f(n) \le n + 2012$ for all $n$.
Prove that for any natural number $n$ and any prime $p$, if $p$ divides $f(n)$ then $p$ divides $n$.
a. $f(m)$ and $f(n)$ are relatively prime whenever $m$ and $n$ are relatively prime.
b. $n \le f(n) \le n + 2012$ for all $n$.
Prove that for any natural number $n$ and any prime $p$, if $p$ divides $f(n)$ then $p$ divides $n$.