Now showing items 1-17 of 17

• #### Balancing Diophantine triples with distance 1 ﻿

For a positive real number let the Balancing distance be the distance from to the closest Balancing number. The Balancing sequence is defined by the initial values , and by the binary recurrence relation , . In this paper, ...
• #### BALANCING WITH BALANCING POWERS ﻿

(UNIV MISKOLC INST MATH, 2013)
In this paper, the Diophantine equation B-1(k) + B-2(k) + ... + B-n-1(k) = B-n+1(k) + B-n+2(k) + ... + B-n+r(l) + for the positive integer unknowns n >= 2, k, l and r is studied in certain cases, where B-n denotes the nth ...
• #### BINOMIAL IDENTITIES INVOLVING THE GENERALIZED FIBONACCI TYPE POLYNOMIALS ﻿

(CHARLES BABBAGE RES CTR, 2011)
We present some binomial identities for sums of the bivariate Fibonacci polynomials and for weighted sums of the usual Fibonacci polynomials with indices in arithmetic progression.
• #### Decompositions of the Cauchy and Ferrers-Jackson polynomials ﻿

(UNIV OSIJEK, DEPT MATHEMATICS, 2016)
Recently, Witula and Slota have given decompositions of the Cauchy and Ferrers-Jackson polynomials [Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence ...
• #### DIOPHANTINE TRIPLES AND REDUCED QUADRUPLES WITH THE LUCAS SEQUENCE OF RECURRENCE ﻿

(CROATIAN MATHEMATICAL SOC, 2014)
In this study, we show that there is no positive integer triple {a, b, c} such that all of ab+1, ac+1 and bc+1 are in the sequence {u(n)}n= 0 satisfies the recurrence un=Aun-1-un-2 with the initial values u0=0, u1=1. ...
• #### FAREY-PELL SEQUENCE, APPROXIMATION TO IRRATIONALS AND HURWITZ'S INEQUALITY ﻿

(INT CENTER SCIENTIFIC RESEARCH & STUDIES, 2016)
The purpose of this paper is to give the notion of Farey-Pell sequence. We investigate some identities of the Farey-Pell sequence. Finally, a generalization of Farey-Pell sequence and an approximation to irrationals via ...

• #### İleri itme ve geri çekme çaprazlanmış polimodüller ﻿

(Niğde Ömer Halisdemir Üniversitesi / Fen Bilimleri Enstitüsü, 2018)
Bu yüksek lisans tezinde, Murat ALP ve Bijan DAVVAZ tarafından  tanımlanan ileri itme ve geri çekme çaprazlanmış polimodüller hakkında bilgi verilmesi amaçlanmıştır. İlk olarak çaprazlanmış modül kavramı incelenmiştir. ...
• #### On solutions of the simultaneous Pell equations and x(2) - (a(2)-1) y(2)=1 and y(2) - pz(2)=1 ﻿

(SPRINGER, 2016)
Let be an integer and p prime number. It is well-known that the solutions of the Pell equation have recurrence relations. For the simultaneous Pell equations x(2) - (a(2) - 1) y(2) = 1 y(2) - pz(2) = 1 assume that and . ...
• #### Özel sayı dizilerinin kombinatoriyal ispatları ﻿

(Niğde Ömer Halisdemir Üniversitesi / Fen Bilimleri Enstitüsü, 2017)
Bu yüksek lisans tezi üç ana başlıktan oluşmaktadır. Birinci bölümde Fibonacci ve Lucas sayılarının tanımları ve özelliklerinden bahsederken, ikinci ve üçüncü bölümde Fibonacci ve Lucas sayılarının kombinatoriyal ...
• #### PELLANS SEQUENCE AND ITS DIOPHANTINE TRIPLES ﻿

(PUBLICATIONS L INSTITUT MATHEMATIQUE MATEMATICKI, 2016)
We introduce a novel fourth order linear recurrence sequence {S-n} using the two periodic binary recurrence. We call it "pellans sequence" and then we solve the system ab + 1 = S-x, ac + 1 = S-y bc + 1 = S-z where a < b < ...
• #### Reciprocal sums of l-th power of generalized binary sequences with indices ﻿

(CHARLES BABBAGE RES CTR, 2008)
Recently in , the author considered certain reciprocal sums of general second order recurrence {W-n}. In this paper, we generalize the results of Xi and we give some new results for the reciprocal sums of l-th power of ...
• #### Reduced diophantine quadruples with the binary recurrence G(n) = AG(n-1) - G(n-2) ﻿

(OVIDIUS UNIV PRESS, 2015)
Given a positive integer A not equal 2. In this paper, we show that there do not exist two positive integer pairs {a, b} not equal {c, d} such that the values of ac + 1, ad + 1 and bc + 1, bd + 1 are the terms of the ...
• #### SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES ﻿

(HACETTEPE UNIV, FAC SCI, 2013)
In this study, we define a generalization of Lucas sequence {p(n)}. Then we obtain Binet formula of sequence {p(n)}. Also, we investigate relationships between generalized Fibonacci and Lucas sequences.