Remark

Tag 06XK, permanent. Cite it as [Bourbaki, Tag 06XK].

Prop. 7 of VI, p. 10 also shows that a necessary and sufficient condition for $x$ and $y$ to be coprime is that $x + y = \sup(x, y)$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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