Recall that an integer is said to be square-free if it is not divisible by the square of any prime. Prove that for any positive integer $n$, there exist $n$ consecutive nonsquare-free positive integers.
Having a lot of trouble with this problem, I tried searching this question up but only got problems similar to it and it still didn't quite help. We are currently covering a section on The Chinese Remainder Theorem. Our teacher showed us two ways of utilizing this theorem, one via back-substitution and one via the classical approach. Looking through my notes I don't see anything resembling this problem, any help is really appreciated.