Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415719 | Journal of Number Theory | 2011 | 18 Pages |
Abstract
A Fibonacci integer is an integer in the multiplicative group generated by the Fibonacci numbers. For example, 77=21â 55/(3â 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(logx)1/2â(logx)ϵ) and exp(c(logx)1/2+(logx)1/6+ϵ), for an explicitly determined constant c. The proof is based on both combinatorial and analytic arguments.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Florian Luca, Carl Pomerance, Stephan Wagner,