منابع مشابه
Fibonacci Integers
A Fibonacci integer is an integer in the multiplicative group generated by the Fibonacci numbers. For example, 77 = 21 · 55/(3 · 5) is a Fibonacci integer. Using some results about the structure of this multiplicative group, we determine a near-asymptotic formula for the counting function of the Fibonacci integers, showing that up to x the number of them is between exp(c(log x) − (log x)) and e...
متن کاملFibonacci Expansions and "f-adic" Integers
A Fibonacci expansion of a nonnegative integer n is an expression of n as a sum of Fibonacci numbers Fk with k > 2. It may be thought of as a partition of n into Fibonacci parts. The most commonly studied such expansion is the unique one in which the parts are all distinct and no two consecutive Fibonacci numbers appear. C. G. Lekkerkerker first showed this expansion was unique in 1952 [5]. The...
متن کاملOn representations of positive integers in the Fibonacci base
We exhibit and study various regularity properties of the sequence (R(n))n 1 which counts the number of different representations of the positive integer n in the Fibonacci numeration system. The regularity properties in question are observed by representing the sequence as a two-dimensional array consisting of an infinite number of rows L1, L2, L3, . . . where each Lk contains fk−1 (the k − 1s...
متن کاملIntegers with a maximal number of Fibonacci representations
We study the properties of the function R(n) which determines the number of representations of an integer n as a sum of distinct Fibonacci numbers Fk. We determine the maximum and mean values of R(n) for Fk ≤ n < Fk+1. Mathematics Subject Classification. 11A67, 11B39.
متن کامل1 INTEGERS 11 A ( 2011 ) Proceedings of Integers Conference 2009 ON THE INTERSECTIONS OF FIBONACCI , PELL , AND LUCAS NUMBERS
We describe how to compute the intersection of two Lucas sequences of the forms {Un(P,±1)}n=0 or {Vn(P,±1)}n=0 with P ∈ Z that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers. We prove that such an intersection is finite except for the case Un(1,−1) and Un(3, 1) and the case of two V -sequences when the product of their discriminants is a perfect square. Moreover, the inter...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2011
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2010.09.010