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clean up phrasing. Based on tag also adding explicit question about if previously conjectured.

Is it a known property of positive integers $n> 2 $ that one must have $n < rad(n(n-1)(n-2))$?

Let $P(n)$ be the statement that $n < rad(n(n-1)(n-2))$

I checked that $P(n)$ holds for $3 \le n \le 3.10^7$: $$n < rad(n(n-1)(n-2))$$

My question: Is $P(n)$ true for any positive integer $n \geq 3$?

Also, is this a pre-existing conjecture?

asked Sep 26, 2019 at 15:41