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Browsing Matematik / Mathematics by Author "Keskin, Refik"

Browsing Matematik / Mathematics by Author "Keskin, Refik"

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  • A NOTE ON SOME DIOPHANTINE EQUATIONS 
    Keskin, Refik; Merve Guney Duman (UNIV MISKOLC INST MATH, 2017)
    Let k >= 3 be an odd integer. In this paper we investigate all positive integer solutions of the equations x(4) - kx(2) y + y(2) = -/+ A, x(4) kx(2) y + y(2) = -/+ A(k(2) - 4), x(4) - (k(2) - 4)y(2) = -/+ 4A, and x(2) - ...
  • A note on some Fuchsian groups 
    Keskin, Refik (SPRINGER, 2005)
    In this paper, we introduce some Fuchsian groups and calculate their parabolic class numbers. In addition, we give two conjectures concerning with the parabolic class number.
  • A note on some subgroups of PSL(2,C) 
    Keskin, Refik (WORLD SCIENTIFIC PUBL CO PTE LTD, 2003)
    In this paper, we introduce some discrete subgroups of PSL(2, C) and determine the number of cusps of 3-manifolds associated to those groups.
  • A. note on some modular subgroups 
    Keskin, Refik (ROCKY MT MATH CONSORTIUM, 2005)
    In this study, we introduce some modular subgroups and we calculate parabolic class numbers of those groups. In addition to this, we gave a nice formula for the parabolic class number of Gamma(0)(n(2)).
  • Fibonacci and Lucas Congruences and Their Applications 
    Keskin, Refik; Demirtürk Bitim, Bahar (SPRINGER HEIDELBERG, 2011)
    In this paper we obtain some new identities containing Fibonacci and Lucas numbers. These identities allow us to give some congruences concerning Fibonacci and Lucas numbers such as L2mn+k equivalent to (-1)((m+1)n) L-k ...
  • Generalized Fibonacci and Lucas numbers of the form 5x(2) 
    Keskin, Refik; Karaatlı, Olcay (WORLD SCIENTIFIC PUBL CO PTE LTD, 2015)
    Let (U-n(P, Q) and (V-n(P, Q) denote the generalized Fibonacci and Lucas sequences, respectively. In this study, we assume that Q = 1. We determine all indices n such that U-n = 5 square and U-n = 5U(m)square under some ...
  • GENERALIZED FIBONACCI AND LUCAS NUMBERS OF THE FORM wx(2) AND wx(2) 1 
    Keskin, Refik (KOREAN MATHEMATICAL SOC, 2014)
    Let P >= 3 be an integer and let (U-n) and (V-n) denote generalized Fibonacci and Lucas sequences defined by U-0 = 0,U-1 = 1; V-0 = 2,V-1 = P, and Un+1 = PUn Un-1 Vn+1 = PVn - Vn-1 for n >= 1. In this study, when P is odd, ...
  • Generalized Fibonacci numbers of the form 
    Keskin, Refik; Öğüt, Ümmügülsüm (SPRINGER, 2016)
    Let be an integer and let and denote generalized Fibonacci and Lucas sequences defined by ; and , for In this study, when P is odd, we solve the equation for After then, we solve some Diophantine equations utilizing solutions ...
  • GENERALIZED FIBONACCI NUMBERS OF THE FORM 11x(2) 
    Öğüt, Ümmügülsüm; Keskin, Refik (HONAM MATHEMATICAL SOC, 2018)
    Let P >= 3 be an integer and let (U-n) denote generalized Fibonacci sequence defined by U-0 = 0, U-1 = 1 and Un+1 = PUn - Un-1 for n >= 1. In this study, when P is odd, we solve the equation U-n = 11x(2) + 1. We show that ...
  • GENERALIZED LUCAS NUMBERS OF THE FORM 5kx(2) AND 7kx(2) 
    Karaatlı, Olcay; Keskin, Refik (KOREAN MATHEMATICAL SOC, 2015)
    Generalized Fibonacci and Lucas sequences (U-n) and (V-n) are defined by the recurrence relations Un+1 = PUn +QU(n-1) and Vn+1 = PVn + QV(n-1), n >= 1, with initial conditions U-0 = 0, U-1 = 1 and V-0 = 2, V-1 = P. This ...
  • Integral points on the elliptic curve y(2) = x(3)+27x-62 
    Karaatlı, Olcay; Keskin, Refik (SPRINGEROPEN, 2013)
    We give a new proof that the elliptic curve y(2) = x(3) + 27x - 62 has only the integral points (x, y) = (2, 0) and (x, y) = (28,844,402, +/- 15,491,585,540) using elementary number theory methods and some properties of ...
  • On some Diophantine equations 
    Demirtürk Bitim, Bahar; Keskin, Refik (SPRINGEROPEN, 2013)
    for p >= 3 and a square-free integer p(2) - 4. In addition to these, all solutions of some different Diophantine equations such as x(2) - v(2n)xy + y(2) = -(p(2) - 4)u(n)(2), x(2) - v(n)xy + y(2) = -(p(2) - 4), x(2) - ...
  • On square classes in generalized Fibonacci sequences 
    Keskin, Refik (POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN, 2016)
    Let P and Q be nonzero integers. The generalized Fibonacci and Lucas sequences are defined respectively as follows: U0=0,U1=1, V0=2,V1=P and Un+1=PUn+QUn−1, Vn+1=PVn+QVn−1 for n≥1. In this paper, when w∈{1,2,3,6}, for all ...
  • On Suborbital Graphs for the Normalizer of Gamma(0)(N) 
    Keskin, Refik; Demirtürk Bitim, Bahar (ELECTRONIC JOURNAL OF COMBINATORICS, 2009)
    where n>1, v is an element of Q boolean OR {infinity} and T is an elliptic mapping of order k in the normalizer of Gamma(0)(N).
  • On the determination of solutions of simultaneous Pell equations x(2) - (a(2)-1) y(2) = y(2) - pz(2)=1 
    Keskin, Refik; Karaatlı, Olcay; Zafer Siar; Ummugulsum Ogut (SPRINGER, 2017)
    where p is prime and a > 1. Assuming the solutions of the Pell equation x(2) -(a(2) - 1) y(2) = 1 are x = x(m) and y = y(m) with m = 2, we prove that the system (0.1) has solutions only when m = 2 or m = 3. In the case of ...
  • On the Diophantine equation x(2) - kxy plus y(2)-2(n)=0 
    Keskin, Refik; Karaatlı, Olcay (SPRINGER HEIDELBERG, 2013)
    In this study, we determine when the Diophantine equation x (2)-kxy+y (2)-2 (n) = 0 has an infinite number of positive integer solutions x and y for 0 a (c) 1/2 n a (c) 1/2 10. Moreover, we give all positive integer solutions ...
  • ON THE DIOPHANTINE EQUATION x(2)-kxy+y(2)+2(n)=0 
    Keskin, Refik; Karaatlı, Olcay (UNIV MISKOLC INST MATH, 2012)
    In this paper, we determine when the equation in the title has an infinite number of positive integer solutions x and y when 0 <= n <= 10. Moreover, we give all the positive integer solutions of the same equation for 0 <= n <= 10.
  • ON THE LUCAS SEQUENCE EQUATIONS V-n = kV(m) AND U-n = kU(m) 
    Keskin, Refik (ARS POLONA-RUCH, 2013)
    Let P and Q be nonzero integers. The sequences of generalized Fibonacci and Lucas numbers 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 >= 1, ...
  • On The Lucas Sequence Equations V-n=7 square and V-n=7V(m)square 
    Karaatlı, Olcay; Keskin, Refik (SPRINGER, 2018)
    Let P be a nonzero integer and let (U-n) and (V-n) denote Lucas sequences of first and second kind defined by U-0 = 0, U-1 = 1; V-0 = 2, V-1 = P; and Un+1 = PUn + Un-1, Vn+1 = PVn + Vn-1 for n >= 1. In this study, when P ...
  • PARABOLIC CLASS NUMBER OF A SUBGROUP OF THE NORMALIZER OF Gamma(0)(m) 
    Keskin, Refik (UNIV MISKOLC INST MATH, 2012)
    In this study, we introduce a subgroup of the normalizer of Gamma(0)(m) and we calculate parabolic class number of this group.