Category:Square-Free Integers

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This category contains results about integers which are square-free.

Let $n \in \Z$.

Then $n$ is square-free if and only if $n$ has no divisor which is the square of a prime.

That is, if and only if the prime decomposition $n = {p_1}^{k_1} {p_2}^{k_2} \cdots {p_r}^{k_r}$ is such that:

$\forall i: 1 \le i \le r: k_i = 1$