Browsing Matematik / Mathematics by Author "Karaatli, O; Keskin, R;"

Now showing items 1-3 of 3

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 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 ...