Problem

Source: The South African Mathematical Olympiad P4

Tags: number theory



Let $A$ be a set of real numbers satisfying the following: (a) $\sqrt(n^2+1) \in A$ for all positive integers $n$, (b) if $x \in A$ and $y \in A$, then $x-y \in A$. Prove that every integer can be written as a product of two different elements in $A$.