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Fibonacci integers |
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| Authors: | Florian Luca |
| Affiliation: | a Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, Mexico b Mathematics Department, Dartmouth College, Hanover, NH 03755, USA c Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, Matieland 7602, South Africa |
| Abstract: | 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  and  , for an explicitly determined constant c. The proof is based on both combinatorial and analytic arguments. |
| Keywords: | Fibonacci numbers Generated group Primitive divisors Counting function Asymptotics |
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