# Catalan's conjecture

- kind: problem
- status: solved (evidence tier V3)
- year: 1844
- authors: Eugène Catalan

**Statement.** 8 and 9 are the only consecutive perfect powers.

Tijdeman showed in 1976 that there are only finitely many solutions, but with a bound too large to search. Mihăilescu finished it with the arithmetic of cyclotomic fields and no computer search at all. The formal-conjectures entry keeps related Diophantine questions open.

*Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.*

Posed 1844, Eugène Catalan. Closed 2002, Preda Mihăilescu.

## Sources

- [Wikipedia: Catalan's conjecture](https://en.wikipedia.org/wiki/Catalan%27s_conjecture)

[Number theory](/wiki/Space:number-theory.md) · [Mathematics](/wiki/Continent:mathematics.md)

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