0

I just did a proof for $m\mid a\ \land m\mid b\Longrightarrow m\mid (\alpha a+\beta b)$ but it feels a bit weak. Can someone please check it and let me know if it is complete? Thank you in advance.

\begin{align*} m\mid a\ \land m\mid b &\Longrightarrow \exists k_1\in\mathbb Z:a=k_1m\ \land\ \exists k_2\in\mathbb Z:b=k_2m\\ &\Longrightarrow\alpha a+\beta b=\alpha k_1m+\beta k_2m=m(\alpha k_1+\beta k_2)\end{align*}

anankElpis
  • 1,255
NotBadG
  • 19
  • 2
    Welcome to MSE. I'm not clicking on a link from a new user nor do I recommend anyone else do so either. Please look over the MathJax tutorial again. – Mike Apr 10 '22 at 15:56
  • It is correct, and works in any ring - see the dupe. Please delete the dupe question. – Bill Dubuque Apr 10 '22 at 16:29

0 Answers0