Finite groups of deficiency zero involving the Lucas numbers

Some New Finite Sums Involving Generalized Fibonacci And Lucas Numbers

On the Structure of Some Deficiency Zero Groups

Groups of deficiency zero

We make a systematic study of groups of deeciency zero, concentrating on groups of prime-power order. We prove that a number of p-groups have deeciency zero and give explicit balanced presentations for them. This signiicantly increases the number of such groups known. We describe a reasonably general computational approach which leads to these results. We also list some other nite groups of dee...

Equations Involving Arithmetic Functions of Fibonacci and Lucas Numbers

For any positive integer k, let (k) and a(k) be the number of positive integers less than or equal to k and relatively prime to k and the sum of divisors ofk, respectively. In [6] we have shown that 0(Fn) > F^n) and that a(Fn) < Fa{ri) and we have also determined all the cases in which the above inequalities become equalities. A more general inequality of this type was proved in [7]. In [8] ...

Some Trigonometric Identities Involving Fibonacci and Lucas Numbers

In this paper, using the number of spanning trees in some classes of graphs, we prove the identities: Fn = 2n−1 n √