Zeckendorf's Theorem

The sequence {F_n-1} is complete even if restricted to subsequences which contain no two consecutive terms, where F_n is a Fibonacci number.

See also

Fibonacci Dual Theorem, Zeckendorf Representation

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Brown, J. L. Jr. "Zeckendorf's Theorem and Some Applications." Fib. Quart. 2, 163-168, 1964.Keller, T. J. "Generalizations of Zeckendorf's Theorem." Fib. Quart. 10, 95-112, 1972.Lekkerkerker, C. G. "Voorstelling van natuurlijke getallen door een som van Fibonacci." Simon Stevin 29, 190-195, 1951-52.

Referenced on Wolfram|Alpha

Zeckendorf's Theorem

Cite this as:

Weisstein, Eric W. "Zeckendorf's Theorem." From MathWorld--A Wolfram Web Resource.

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