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Integer solutions of some Diophantine equations via Fibonacci and Lucas numbers.
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. UsingExpand
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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 allExpand
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Some New Properties of Balancing Numbers and Square Triangular Numbers
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 balancingExpand
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On the Diophantine equation x2 − kxy + y2 − 2n = 0
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 integerExpand
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Some new Fibonacci and Lucas identities by matrix methods
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
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 , 402Expand
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Suborbital graphs for the normalizer of Gamma0(m)
  • R. Keskin
  • Computer Science, Mathematics
  • Eur. J. Comb.
  • 1 February 2006
TLDR
In this study, we characterize all circuits in the suborbital graph for the normalizer of Γ0(m) when m is a square-free positive integer. Expand
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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 congruencesExpand
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GENERALIZED FIBONACCI AND LUCAS NUMBERS OF THE FORM wx2AND wx2∓ 1
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 thisExpand
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