After defining a class of generalized Fibonacci numbers and Lucas numbers, we characterize the Fibonacci pseudoprimes of the mth kind. In virtue of the apparent paucity of the composite numbers which are Fibonacci pseudoprimes of the mth kind for distinct values o f the integral parameter m , a method, which we believe to be new, for finding large probable primes is proposed. An efficient compu...

The purpose of this paper is to investigate the calculation of Fibonacci numbers using the Chinese Remainder Theorem (CRT). This paper begins by laying down some general conclusions that can be made about the Fibonacci sequence. It will then go into specific cases of the CRT and how to calculate Fibonacci numbers with reduced forms of the CRT equations. For each of the cases, algorithms and ana...

To parallelize applications that require the use of random numbers, an efficient and good quality parallel random number generator is required. In this paper, we study the parallelization of lagged Fibonacci generators for distributed memory parallel computers. Two popular ways of generating a random sequence in parallel are studied: the contiguous subsequence technique and the leapfrog techniq...

The Fibonacci sequence {Fn} is defined by the recurrence relation Fn = Fn−1+ Fn−2, for n ≥ 2 with F0 = 0 and F1 = 1. The Lucas sequence {Ln} , considered as a companion to Fibonacci sequence, is defined recursively by Ln = Ln−1 + Ln−2, for n ≥ 2 with L0 = 2 and L1 = 1. It is well known that F−n = (−1)Fn and L−n = (−1)Ln, for every n ∈ Z. For more detailed information see [9],[10]. This paper pr...

The popular hypercube interconnection network has high wiring(VLS1) complexity. The reduced hypercube (RH) is obtained by a uniform reduction in the number of channels for each hypercube node in order io reduce the VLSI complexity. It is known that the RH achieves performance comparable to that of the hypercube, at much lower hardware cost, through hypercube emulation. The reduced complexity of...

The linear complexity and the k-error linear complexity of a sequence are important security measures for key stream strength. By studying sequences with minimum Hamming weight, a new tool called hypercube theory is developed for p-periodic binary sequences. In fact, hypercube theory is very important in investigating critical error linear complexity spectrum proposed by Etzion et al. To demons...

We have measured the angular dependence of ferromagnetic resonance (FMR) spectra for Fibonacci-distorted, Kagome artificial spin ice (ASI). The number strong modes in FMR depend on orientation applied DC magnetic field. In addition, discontinuities observed field-frequency dispersion curves also field orientation, and signal a multi-step magnetization reversal, which is caused by reduced energy...

We propose new deadlock-free routing and broadcasting algorithms for incomplete hypercube network that have optimal communication and computation time. Broadcasting algorithm may run on one-port communication model of hypercube and is suitable for both the asynchronous (MIMD, or distributed) and synchronous (SIMD, or parallel) hypercube models. Routing and broadcasting procedures have optimal d...

The combinatorial properties of the Fibonacci innnite word are of great interest in some aspects of mathematics and physics, such as number theory, fractal geometry, formal language, computational complexity , quasicrystals etc. In this note, we introduce the singular words of the Fibonacci innnite word and discuss their properties. We establish two decompositions of the Fibonacci word in singu...

Double Fibonacci sequences (xn,k) are introduced and they are related to operations with Fibonacci modules. Generalizations and examples are also discussed.