Question 144
Let $a$, $b$ be positive real numbers with $b - a \gt 2$. Prove that for any two distinct integers $m$, $n$ in the interval $[a, b)$, there is a nonempty set $S$ consisting of some integers in the interval $[ab, (a+1)(b+1))$, such that $\frac{\prod x}{mn}$ is a square of a rational number. (Posed by Yu Hongbing)