How do I know if a theorem has been proposed and proved

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I'm trying to write a paper where the proof requires some theorems. I can prove these theorems myself, but I don't know if they have already been proved, and if so I only need to quote them. Is there any alternative to reading more papers? Or there's nothing wrong with having theorems that have already been proven in a paper? I wasn't a math major, and the teachers couldn't guide me.

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I’d say to definitely look through Google scholar, and also textbooks in the relevant fields depending on the level of the problems you’re working on. (If you’re not sure what the level of the problem is, that’s probably a sign that you need to learn more about the field from some textbooks).

I’ll also drop this link to some advice from Henry Cohn on writing papers as well, and how the publication process generally works. You might benefit from it, especially if you don’t have teachers who are able to guide you.