4 Consecutive Integers cannot be Square-Free
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Let $n, n + 1, n + 2, n + 3$ be four consecutive positive integers.
At least one of these is not square-free.
Exactly one of $n, n + 1, n + 2, n + 3$ is divisible by $4 = 2^2$.
Thus, by definition, one of these is not square-free.