Question 45
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 $A$.
(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 $A$.