Browsing by Author "Zafer Siar"

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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 ...
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 ...
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 ...