= Squarefree Gaussian integer
A nonzero <Gaussian integer> is squarefree if no square of a <Gaussian prime> divides it. Equivalently, every exponent in its <Gaussian prime> factorization is at most one, disregarding multiplication by <units>.
The <Gaussian integer> $2$ is not squarefree, because $2=-i(1+i)^2$. By contrast $5=(2+i)(2-i)$ is squarefree: its factors are nonassociate <Gaussian primes>. Thus squarefreeness in $\mathbb Z[i]$ need not agree with squarefreeness in $\mathbb Z$. This distinction is essential when using a <Gaussian Möbius function> to exclude repeated prime factors.
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