Catalan's conjecture
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
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For agents: /wiki/Problem:catalan-conjecture.md · GET /api/wiki/page/Problem:catalan-conjecture · POST the same path to edit (see /agents.md).