Related papers: Concatenated Fibonacci and Lucas numbers do not fo…

We derive some Fibonacci and Lucas identities which contain inverse binomial coefficients. Extension of the results to the general Horadam sequence is possible, in some cases.

This paper has been withdrawn by the authors

This paper has been withdrawn since the results are not satisfied.

This paper has been withdrawn by the author, due to a crucial error in page 5.

Withdrawn due to critical error.

This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).

Using a straightforward elementary approach, we derive numerous infinite arctangent summation formulas involving Fibonacci and Lucas numbers. While most of the results obtained are new, a couple of celebrated results appear as particular…

This paper has been withdrawn by the author due to incomplete interpretation for the results.

In this paper, we provide new applications of Fibonacci and Lucas numbers. In some circumstances, we find algebraic structures on some sets defined with these numbers, we generalize Fibonacci and Lucas numbers by using an arbitrary binary…

In this paper, we prove that there is no x>=4 such that the difference of x-th powers of two consecutive Fibonacci numbers greater than 0 is a Lucas number.

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

The paper has been withdrawn

The convolved Fibonacci numbers F_j^(r) are defined by (1-z-z^2)^{-r}=\sum_{j>=0}F_{j+1}^(r)z^j. In this note some related numbers that can be expressed in terms of convolved Fibonacci numbers are considered. These numbers appear in the…

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

We considered the properties of generalized Fibonacci and Lucas numbers class. The analogues of well-known Fibonacci identities for generalized numbers are obtained. We gained a new identity of product convolution of generalized Fibonacci…

This paper has been withdrawn by the author, due to a significant error in section 4.3.1.

Major mistake. The paper has been withdrawn.

This paper has been withdrawn by the author, due to an error in the proof of lemma 7.4. However, numerical evidence strongly suggest that this lemma is true.

This paper is withdrawn due to some errors, which are corrected in arXiv:0912.0071v4 [cs.LG].

This paper has been withdrawn by the auther due to an error