The only solution in natural numbers greater than one of the equation x to the p minus y to the q equals one is 3 squared minus 2 cubed equals one. Proved by Preda Mihailescu in 2002, it resolved Catalan's conjecture, which had stood open since 1844.
Facts
StatementThe only solution in natural numbers greater than one of x^p minus y^q equals one is 3 squared minus 2 cubed equals one; that is, 8 and 9 are the only two consecutive perfect powers. 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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Sources
1. Mihailescu's Theorem (Wikipedia)
Wikimedia FoundationLead sectionQuote, Lead section
Catalan's conjecture (or Mihăilescu's theorem) is a theorem in number theory that was conjectured by the mathematician Eugène Charles Catalan in 1842 and proven in 2002 by Preda Mihăilescu at Paderborn University.
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