[mahalex]

If we exclude 0, the only solutions are 2^1 = 1^2 + 1 and 3^2 = 2^3 + 1

[nmmnthrowaway]

That is correct. Why are there no others?

[mahalex]

Because Catalan’s conjecture.

[yarg]

> Catalan's conjecture was proven by Preda Mihăilescu in April 2002.

Cool, so the conjecture's a theorem.

https://xn--uni-gttingen-8ib.academia.edu/PredaMihailescu

[hgsgm]

Which has an extremely complicated proof :-(

[mahalex]

I wouldn’t call it extremely complicated; it is much simpler than the proof of FLT.

[nmmnthrowaway]

Yes, but there is a much simpler proof.

[judofyr]

Something related to prime factorization maybe?

[AnimalMuppet]

Do tell.