A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...

Let $X$ be a vector space over a field $K$ of real or complex numbers. We will prove the superstability of the following Go{l}c{a}b-Schinzel type equation$$f(x+g(x)y)=f(x)f(y), x,yin X,$$where $f,g:Xrightarrow K$ are unknown functions (satisfying some assumptions). Then we generalize the superstability result for this equation with values in the field of complex numbers to the case of an arbitr...

We continue our study on relationships between Fibonacci (Lucas) numbers and Bernoulli polynomials. The derivations of results are based functional equations for the respective generating functions, which in case combinations hyperbolic functions. Special cases some corollaries will highlight interesting aspects findings.

in this present work, the kudryashov method and the functional variable method are used to construct exact solutions of the complex kdv equation. the kudryashov method and the functional variable method are powerful methods for obtaining exact solutions of nonlinear evolution equations.

INTRODUCTION Let p denote a prime, n a natural number, Fin) the nth Fibonacci number. Consider the equation: F(n) = px, (*) In [3], J. H. E. Cohn proved that for p = 2, the only solutions of (*) are (i) n = 3, x = 1 and (ii) n = 6, x = 4. In [8], R. Steiner proved that for p = 3, the only solution of (*) is n 4, a: = 1. Call a solution of (*) trivial if x = 1 . In this article, we solve O ) for...

The Fibonacci lengths of the finite p-groups have been studied by R. Dikici and co-authors since 1992. All of the considered groups are of exponent p, and the lengths depend on the celebrated Wall number k(p). The study of p-groups of nilpotency class 3 and exponent p has been done in 2004 by R. Dikici as well. In this paper we study all of the p-groups of nilpotency class 3 and exponent p2. Th...

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...

In this paper, we note that a number of unexplained and stipulative properties of the grammar (such as the Generalized Extended Projection Principle, Binary Branching, Labeling) find a functional explanation, if we view them as correlates of a general desire for the grammar to maximize trees in such a way that they result in a Fibonacci-like sequence of maximal categories. Further, we note that...