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