Hello.
The first one is two different computers, in two different locations. Is it possible to share this file so that both machines can see the same documents and edit them?
You cannot edit simultaneously.
If you save the file to a shared drive or cloud location then you can edit from either computer. Frequent changes to security settings mean that sharing a Google Drive location might not work
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Main point is: Do you need access at the same time? If yes, check for Collabora. Their variant allows multiple editors, nut your document will be then at a 3rd place- on a server, not on your local computers.
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As @EarnestAl already wrote, you can sync files. The problem is how to ensure you don’t make changes to both files and how to detect version conflict.
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Why the math tag?
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The tag “common” would be apprpriate.