Results 51 to 60 of about 242,259 (303)
Complete solutions of the simultaneous Pell equations $ (a^2+1)y^2-x^2 = y^2-bz^2 = 1 $
AIMS Mathematics, 2021 In this paper, we consider the simultaneous Pell equations $ (a^2+1)y^2-x^2 = y^2-bz^2 = 1 $ where $ a > 0 $ is an integer and $ b > 1 $ is squarefree and has at most three prime divisors.
Changsheng Luo, Jiagui Luo
doaj +1 more source
On New Polynomial Sequences Constructed to Each Vertex in an n-Gon
Discrete Dynamics in Nature and Society, 2022 In this work, we bring to light the properties of newly formed polynomial sequences at each vertex of Pell polynomial sequences placed clockwise at each vertex in the n-gon. We compute the relation among the polynomials with such vertices.
Abdul Hamid Ganie +3 more
doaj +1 more source
Complete solutions of the simultaneous Pell's equations $ (a^2+2)x^2-y^2 = 2 $ and $ x^2-bz^2 = 1 $
AIMS Mathematics, 2023 In this paper, we consider the simultaneous Pell equations $ (a^2+2)x^2-y^2 = 2 $ and $ x^2-bz^2 = 1 $ where $ a $ is a positive integer and $ b > 1 $ is squarefree and has at most three prime divisors.
Cencen Dou, Jiagui Luo
doaj +1 more source
On the discriminator of Lucas sequences. II
, 2023 25 pages, 7 ...
Ferrari, ., Luca, F., Moree, P.
openaire +3 more sources
Advanced Engineering Materials, EarlyView.This article investigates residual stress formation during single‐spot nanosecond laser ablation of stainless steel. Experimental validation and a parametric study using finite element simulations are employed to analyze thermal effects, ablation dynamics, and stress evolution.
Yutaka Tsumura +7 more
wiley +1 more source
Magic numbers in the music of Sofia Gubaidulina [PDF]
Muzikologija, 2002 Sofia Gubaidulina's compositions are characterized by a special kind of symbolism and constructivism both based on numbers, i.e. mathematical proportions. In almost all her works so-called numerical plots can be detected. The proportions of the Fibonacci
Tsenova Valeria
doaj +1 more source
Advanced Functional Materials, EarlyView.This research applies advanced laser beam shaping (LCoS‐SLM) to fabricate the Ti‐6Al‐4V alloy via laser powder bed fusion. A tailored beam is used to prevent martensite formation and create a dual α+β microstructure by controlling cooling rates.
Reza Esmaeilzadeh +8 more
wiley +1 more source
On the Split Mersenne and Mersenne-Lucas Hybrid Quaternions
مجلة بغداد للعلوم, 2023 In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.
B. Malini Devi, S. Devibala
doaj +1 more source
Lucas sequence, its properties and generalisation [PDF]
, 2013 Fibonacci AND Lucas sequences are most interesting among recurrent sequences.
Barik, Biswajit
core
On harmonic numbers and Lucas sequences [PDF]
Publicationes Mathematicae Debrecen, 2012 Harmonic numbers $H_k=\sum_{05 we have $$\sum_{k=0}^{p-1}u_{k+ }H_k/2^k=0 (mod p),$$ where $ =0$ if p=1,2,4,8 (mod 15), and $ =1$ otherwise.
openaire +3 more sources