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I think I'm missing something here but my lecture notes just seem to state that 'clearly' for $x$ and $y$ in the Gaussian integers (elements of $\mathbb{Z}[i]$, a Euclidean domain), if $\nu(x) = \nu(y)$ then clearly $x$ and $y$ are associates. Am I missing something here or is this obvious?

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    What is $\nu$? Is it the square of the complex absolute value, as Brian assumed?2012-05-15
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    @Hurkyl: Good point: I too assumed $\nu$ was the norm of a Gaussian integer. But what else could it be?2012-05-15
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    So let us wait until the OP dignifies us with an explanation about his/her notation: what is $\,\nu\,$, anyway?2012-05-17

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