Corollary 5

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

Algebra, chapter VI, § 1. Ordered groups. Divisibility

— If d is a gcd of x and y, then $d^n$ is a gcd of $x^n$ and $y^n$ for each positive integer n. Indeed $xd^1$ and $yd^1$ are coprime (Prop. 10 (DIV)), and hence so are $x^n d^{-n}$ and $y^n d^{-n}$ (Cor. 4).

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

Cited by

Nothing.

Cites

Cor. 4
Prop. 10