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Is there an interesting set of natural numbers defined by a number-theoretic property that is finite? (lemmy.sdf.org)

submitted 1 year ago* (last edited 1 year ago) by [email protected] to c/[email protected]

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[–] zipsglacier 5 points 1 year ago (1 children)

There are tons of them! For example, the class of numbers n such that there is a Platonic solid made of n-gons. This class only has the numbers 3, 4, and 5. You can get other examples any time there is an interesting mathematical structure with only finitely many examples.

[–] [email protected] -2 points 1 year ago* (last edited 1 year ago) (1 children)

Well, yes, obviously. I was hoping for something number-theoretic, though. Let me reword the title.

[–] zipsglacier 2 points 1 year ago (1 children)

Haha, ok, how about numbers n such that there are nontrivial solutions to a^n + b^n = c^n

My point is that interesting (non-)existence results give examples of the type I thought you were asking for.

[–] [email protected] 2 points 1 year ago

Oh yeah, Fermat's Last Theorem. I bet I would have thought of that right away if I was a bit older. The Wiefrich primes came up elsewhere here, and they have a kind of similar background.

Thanks for the answers!