Definition:Square-Free Integer
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Definition
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:
- $\forall i: 1 \le i \le r: k_i = 1$
Also see
- Results about square-free integers can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): square-free
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): square-free