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Integer solutions of some Diophantine equations via Fibonacci and Lucas numbers.

- B. Demirtürk, R. Keskin
- Mathematics
- 2009

We study the problem of finding all integer solutions of the Diophantine equations x 2 − 5Fnxy − 5(−1) n y 2 = ±L 2 , x 2 − Lnxy + (−1) n y 2 = ±5F 2 n , and x 2 − Lnxy + (−1) n y 2 = ±F 2 n. Using… Expand

13 3- PDF

Positive integer solutions of some Diophantine equations in terms of integer sequences

In this paper, we define some new number sequences, which we represent as $$ (B_{n}),(b_{n}),(y_{n})$$(Bn),(bn),(yn) and present relations of these new sequences with each other. Then, we give all… Expand

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Some New Properties of Balancing Numbers and Square Triangular Numbers

- R. Keskin, Olcay Karaatlõ
- Mathematics
- 2012

A number N is a square if it can be written as N = n 2 for some natural number n; it is a triangular number if it can be written as N = n(n + 1)/2 for some natural number n; and it is a balancing… Expand

30 1- PDF

On the Diophantine equation x2 − kxy + y2 − 2n = 0

- R. Keskin, Z. Siar, O. Karaatli
- Mathematics
- 10 November 2013

In this study, we determine when the Diophantine equation x2−kxy+y2−2n = 0 has an infinite number of positive integer solutions x and y for 0 ⩽ n ⩽ 10. Moreover, we give all positive integer… Expand

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Some new Fibonacci and Lucas identities by matrix methods

- R. Keskin, B. Demirtürk
- Mathematics
- 15 April 2010

The aim of this article is to characterize the 2 × 2 matrices X satisfying X 2 = X + I and obtain some new identities concerning with Fibonacci and Lucas numbers.

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Integral points on the elliptic curve y 2 = x 3 + 27 x − 62 Open image in new window

- O. Karaatli, R. Keskin
- Mathematics
- 1 December 2013

We give a new proof that the elliptic curve y 2 = x 3 + 27 x − 62 Open image in new window has only the integral points ( x , y ) = ( 2 , 0 ) Open image in new window and ( x , y ) = ( 28 , 844 , 402… Expand

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Suborbital graphs for the normalizer of Gamma0(m)

- R. Keskin
- Computer Science, Mathematics
- Eur. J. Comb.
- 1 February 2006

TLDR

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Some New Identities Concerning Generalized Fibonacciand Lucas Numbers

In this paper we obtain some identities containing generalized Fibonacciand Lucas numbers. Some of them are new and some are well known.By using some of these identities we give some congruences… Expand

34- PDF

GENERALIZED FIBONACCI AND LUCAS NUMBERS OF THE FORM wx2AND wx2∓ 1

- R. Keskin
- Mathematics
- 31 July 2014

Let P ≥ 3 be an integer and let (Un) and (Vn) denote generalized Fibonacci and Lucas sequences defined by U0 = 0, U1 = 1; V0 = 2, V1 = P, and Un+1 = PUn − Un−1, Vn+1 = PVn − Vn−1 for n ≥ 1. In this… Expand

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