We give several identities about Fibonacci and Lucas hybrid numbers. introduce the numbers with negative subscripts. obtain different Cassini for conjugate of by two determinant definitions a square matrix (whose entries are numbers).

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...

The amount of literature bears witness to the ubiquity of the Fibonacci numbers and the Lucas numbers. Not only these numbers are popular in expository literature because of their beautiful properties, but also the fact that they ‘occur in nature’ adds to their fascination. Our purpose is to use a certain polynomial identity to express these numbers in terms of trigonometric functions. It is in...

The aim of the paper is to find some new determinants connected with Fibonacci numbers. We generalize the result provided in Strang’s book because we derive that two sequences of similar tridiagonal matrices are connected with Fibonacci numbers. AMS subject classification: Primary 15A15, 11B39; Secondary 11B37, 11B83.

We give an explicit formula for the figure of merit ρN of 2-dimensional rank 2 lattice rules in terms of continued fractions for rational numbers. Further we generalize Fibonacci lattice rules to rank 2 Fibonacci lattice rules which have the same ratio of the figure of merit to the number of points as the classical Fibonacci lattice rule.