**Definition:**A whole number is free of squares if it is not divisible by the square of any whole number greater than $ 1 $.
Consider the next arbitrary interval of consecutive integers $ (m + 1, m + 2, \ldots, m + (n-1), m + n) $. So, by Chinese remainder theorem we will have to, $$\left\{\begin{align*} m&\equiv-1\pmod{2^2}\\ m&\equiv-2\pmod{3^2}\\ m&\equiv-3\pmod{5^2}\\ m&\equiv-4\pmod{7^2}\\ &\;\;\vdots\\ m&\equiv-n\pmod{p_n^2} \end{align*}\right.$$ Thus, we have found arbitrarily large intervals which are divisible by the square of an integer greater than $ 1 $. This ends the test. It's okay?