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Browsing Matematik / Mathematics by Author "Keskin, Refik"

Now showing items 21-32 of 32

Positive integer solutions of the diophantine equation x(2)-L(n)xy +(-1)(n)y(2) = +/- 5(r)

Keskin, Refik (SPRINGER INDIA, 2014)

In this paper, we consider the equation x (2)-L (n) x y+(-1) (n) y (2) = +/- 5 (r) and determine the values of n for which the equation has positive integer solutions x and y. Moreover, we give all positive integer solutions ...
POSITIVE INTEGER SOLUTIONS OF THE DIOPHANTINE EQUATIONS x(2)-5F(n)(xy)-5(-1)(n)y(2) = +/- 5(r)

Keskin, Refik; Karaatlı, Olcay (UNIV MISKOLC INST MATH, 2013)

In this study, we consider the Diophantine equations given in the title and determine when these equations have positive integer solutions. Moreover, we find all positive integer solutions of them in terms of Fibonacci and ...
Proof of a conjecture related to the parabolic class numbers of some Fuchsian groups

Keskin, Refik (ELSEVIER SCIENCE INC, 2005)

This paper proves a conjecture given in [6], which is concerning with the parabolic class numbers of some Fuchsian groups.
Pythagorean triples containing generalized Lucas numbers

Zafer Siar; Keskin, Refik (SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, 2018)

Let P and Q be nonzero integers. Generalized Fibonacci and Lucas sequences are defined as follows: U-0(P, Q) = 0, U-1(P, Q) = 1, and Un+1(P, Q) = PUn(P, Q)+QU(n-1)(P, Q) for n >= 1 and V-0(P, Q) = 2, V-1(P, Q) = P, and ...
Solutions of Some Diophantine Equations Using Generalized Fibonacci and Lucas Sequences

Keskin, Refik; Demirtürk Bitim, Bahar (CHARLES BABBAGE RES CTR, 2013)

In this study, we deal with some Diophantine equations. By using the generalized Fibonacci and Lucas sequences, we obtain all integer solutions of some Diophantine equations such as x(2) - kxy - y(2) = -/+ 1, x(2) - kxy + ...
Solutions of some quadratic Diophantine equations

Keskin, Refik (PERGAMON-ELSEVIER SCIENCE LTD, 2010)

In this study, we investigate positive integer solutions of the Diophantine equations x(2) - kxy(sic)y(2)(sic)x = 0 and x(2)-kxy-y(2)(sic)y = 0. It is shown that when k > 3,x2-kxy+y(2)+x = 0 has no positive integer solutions ...
SOME NEW IDENTITIES CONCERNING GENERALIZED FIBONACCI AND LUCAS NUMBERS

Keskin, Refik (HACETTEPE UNIV, FAC SCI, 2013)

U2mn+r equivalent to (-t)(mn) U-r (mod U-m).
SOME NEW IDENTITIES CONCERNING GENERALIZED FIBONACCI AND LUCAS NUMBERS

Keskin, Refik (HACETTEPE UNIV, FAC SCI, 2013)

U2mn+r equivalent to (-t)(mn) U-r (mod U-m).
Suborbital graphs for the normalizer of Gamma(0)(m)

Keskin, Refik (ACADEMIC PRESS LTD ELSEVIER SCIENCE LTD, 2006)

In this study, we characterize all circuits in the suborbital graph for the normalizer of Gamma(0) (m) when in is a square-free positive integer. We propose a conjecture concerning the suborbital graphs. (C) 2004 Elsevier ...
SUM FORMULAE OF GENERALIZED FIBONACCI AND LUCAS NUMBERS

Zvonko Cerin; Demirtürk Bitim, Bahar; Keskin, Refik (HONAM MATHEMATICAL SOC, 2018)

In this paper we obtain some formulae for several sums of generalized Fibonacci numbers U-n and generalized Lucas numbers V-n and their dual forms G(n) and H-n by using extensions of an interesting identity by A. R. Amini ...
THE SQUARE TERMS IN GENERALIZED LUCAS SEQUENCE WITH PARAMETERS P AND Q

Zafer Siar; Keskin, Refik (MATEMATISK INST, 2016)

Let P and Q be nonzero integers. Generalized Lucas sequence is defined as follows: V-0 = 2, V-1 = P and Vn+1 = PVn QV(n-1) for n >= 1. We assume that P and Q are odd relatively prime integers. Firstly, we determine all ...
THE SQUARE TERMS IN GENERALIZED LUCAS SEQUENCES

Keskin, Refik (LONDON MATH SOC, 2014)

Let P and Q be non-zero integers. The generalized Fibonacci sequence {U-n} and Lucas sequence {V-n} are defined by U-0 = 0, U-1 = 1 and Un+1 = PUn + QU(n-1) for n >= 1 and V-0 = 2, V-1 = P and Vn+1 = PVn + QV(n-1) for n ...