Every positive integer can be represented uniquely as a sum of one or more non-consecutive Fibonacci numbers. Proved by Edouard Zeckendorf, it gives a natural positional numeral system built from the Fibonacci sequence.
Facts
StatementEvery positive integer can be represented uniquely as a sum of one or more Fibonacci numbers such that the sum includes no two consecutive Fibonacci numbers; this sum is the number's Zeckendorf representation. 2 Classification
Statement Form Connections
Has Statement Form
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.
In Branch
Sources
1. Wikipedia: Zeckendorf's theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
It states that every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.
2. Zeckendorf's Theorem (Wikipedia)
Wikimedia FoundationReferences sectionQuote, References section
Zeckendorf, E. (1972). "Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas". Bull. Soc. R. Sci. Liège (in French). 41: 179-182.
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