Talk:Integers Coprime to Zero

The fact is the situation where both $m$ and $n$ are zero is covered, at the bottom of the page.

As for the other point, I don't know what the problem is. --prime mover (talk) 09:49, 3 September 2022 (UTC)


 * Sorry, where is the situation defined? Especially, where is $0 \perp 0$ defined? We need a correct citation.
 * The other point is similar. What should be $\gcd \set{n,0}$ is $n=0$? Where is this defined?--Usagiop (talk) 10:23, 3 September 2022 (UTC)
 * We need to assume $n \in \Z_{\ne 0}$.--Usagiop (talk) 10:25, 3 September 2022 (UTC)


 * Definition:Coprime Integers defines when $m,n$ are coprime for $m \ne 0$ or $n \ne 0$. I would argue that since it is not defined what $0$ is comprime to $0$ should mean, it follows that $0$ is not coprime to $0$. I understand that the suggestion is we should not write $n \perp 0$ while letting $n \in \Z$, but I do not think it is wrong.
 * Second, the proof directly mentions that $\gcd \set {n, 0}$ is not defined. --Anghel (talk) 11:21, 3 September 2022 (UTC)


 * I got your point, but the exposition should be improved. This is very hard to understand. In your opinion, the following claim is also true:
 * $n \in \C: n \perp 0 \iff n \in \set {1, -1}$
 * I would say this is wrong.--Usagiop (talk) 17:24, 3 September 2022 (UTC)