Square-free integer - Knowlpedia

A nonzero integer $d$ is square-free if the only positive integer $m$ for which $m^2$ divides $d$ is $m=1$ . Equivalently, no prime square divides $d$ .

Examples

The integers $1,2,3,5,6$ are square-free; $12$ is not, since $4\mid12$ . The sign makes no difference. Zero is excluded.

Quadratic-field parameters

Removing square factors gives $\mathbb Q(\sqrt{-12})=\mathbb Q(\sqrt{-3})$ . Using a positive square-free parameter avoids describing the same imaginary quadratic field repeatedly.