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The extension of the D(-k)-pair k, k+1 to a quadruple

Periodica Mathematica Hungarica, 2022
Let $$n\ne 0$$ n ≠ 0 be an integer. A set of m distinct positive integers $$\{a_1,a_2,\ldots ,a_m\}$$ { a 1 , a 2 , … , a m } is called a D ( n )- m -tuple if $$a_ia_j + n$$ a i a j + n is a perfect square for all $$1\le i < j \le m$$ 1 ≤ i < j ≤ m . Let
Nikola Adžaga, A. Filipin, Y. Fujita
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Solving Problems with Bounds on Linear Forms in Logarithms

Journal of High School Research
This expository paper explores the theory of linear forms in logarithms and its applications to Diophantine equations. We begin with foundational results on transcendental numbers, including Liouville's theorem and the Gelfond-Schneider theorem, before ...
K. Agrawal
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On the Fibonacci numbers and their sums which are close to a power of 3

Gulf Journal of Mathematics
Let (Ln)n ≥ 0 be the Lucas sequence defined by Ln+2 = Ln+1 + Ln for all n ≥ 0, with initial values L0 = 2 and L1 = 1. In this paper, we find all the Fibonacci numbers 2Fn and sums of two Fibonacci numbers which are close to a power of 3.
Anouar Gaha, Soufiane Mezroui
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Two Problems on Narayana Numbers And Repeated Digit Numbers

Punjab University journal of mathematics
This work aims to solve two problems in the Diophantine equation of the Narayana sequence. In the first question it’s proven that there are only 177 solutions of expressing the product of two Narayana numbers as b repdigits numbers, for base 2 ≤ b ≤ 50 ...
A. Elsonbaty, G. Abou-Elela, M. Anwar
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Solutions of Two Diophantine Equations Pl = Jr + Js and Rl = Jr + Js

Punjab University journal of mathematics
Suppose that the sequences {Pi}i≥0 , {Ri}i≥0 , and {Ji}i≥0 correspond to the Padovan numbers, Perrin numbers, and Jacobsthal numbers, respectively.
Mustafa Ismail   +3 more
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Sums of Tribonacci numbers close to powers of 2

Mathematica Slovaca
The Tribonacci sequence (Tn)n > 0 is a generalization of the Fibonacci sequence whose first terms are 0, 1, 1 and each term afterwards is the sum of the three preceding terms. The present paper combines Baker’s theory of linear forms in logarithms with a
Jhon J. Bravo
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