Question 192
Prove that there exist two positive real numbers $C$ and $\alpha \gt \frac{1}{2}$, such that, for any positive integer $n$, there is a subset $A$ of $\{1, 2, \dots, n\}$ with $|A| \ge Cn^\alpha$, such that the difference between any pair of different numbers in $A$ is not a perfect square.