What is the ANZL Algorithm? It is a genuine result of our work which is theoretically and practically proved. By using the ANZL Algorithm, we can test whether a given number belongs to Lucas’s series. It can also be used to find a sequence of Lucas’s numbers, starting from any number . If a given number completes the relation , we can say that it is a Lucas number and we mark it as . From the p...

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...

This article provides the first bijective proof for a previously “uncounted” Fibonacci number identity of Vajda. Bijections on similar sets that illustrate a related family of Fibonacci number identities are also considered.

We show that if w is a factor of the infinite Fibonacci word, then the least period of w is a Fibonacci number.