this post was submitted on 18 Aug 2023
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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!