A beautiful theorem of Zeckendorf states that every integer can be written uniquely as a sum
of non-consecutive Fibonacci numbers [Formula: see text]. Lekkerkerker (1951–1952)[13] …

Text A beautiful theorem of Zeckendorf states that every positive integer can be uniquely
decomposed as a sum of non-consecutive Fibonacci numbers {F n}, where F 1= 1, F 2= 2 …

The Zeckendorf decomposition of a positive integer n is the unique set of nonconsecutive
Fibonacci numbers that sum to n. Baird-Smith, et al., defined a game on Fibonacci …

Zeckendorf proved that every positive integer n can be written uniquely as the sum of non-
adjacent Fibonacci numbers; a similar result, though with a different notion of a legal …

The Zeckendorf representation, using sums of Fibonacci numbers, is widely known Fraenkel
generalized to recurrence sequences un= a 1 un− 1+⋯+ ahun− h provided a 1≥ a 2≥⋯≥ …

Zeckendorf proved any integer can be decomposed uniquely as a sum of non-adjacent
Fibonacci numbers, F n. Using continued fractions, Lekkerkerker proved the average …

An interesting characterization of the Fibonacci numbers is that if we write them as F 1= 1, F
2= 2, F 3= 3, F 4= 5,…, then every positive integer can be written uniquely as a sum of non …

By Zeckendorf's theorem, an equivalent definition of the Fibonacci sequence (appropriately
normalized) is that it is the unique sequence of increasing integers such that every positive …

Zeckendorf's Theorem states that any positive integer can be written uniquely as a sum of
non-adjacent Fibonacci numbers; this result has been generalized to many recurrence …

Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of
non-consecutive Fibonacci numbers F n, with initial terms F 1= 1, F 2= 2. We consider the …