Results 21 to 30 of about 53,772 (244)
Solutions of the Diophantine Equations Br=Js+Jt and Cr=Js+Jt
Journal of Mathematics, 2023 Let Brr≥0, Jrr≥0, and Crr≥0 be the balancing, Jacobsthal, and Lucas balancing numbers, respectively. In this paper, the diophantine equations Br=Js+Jt and Cr=Js+Jt are completely solved.
Ahmed Gaber, Mohiedeen Ahmed
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Padovan numbers which are concatenations of three Padovan or Perrin numbers [PDF]
Notes on Number Theory and Discrete MathematicsThis paper presents all Padovan numbers that can be written as the concatenation of three Padovan or Perrin numbers under a certain constraint. Namely, we consider the Diophantine equations Pₜ=10ᵈ⁺ˡPₘ+10ˡPₙ+Pᵣ and Pₜ=10ᵈ⁺ˡRₘ+10ˡRₙ+Rᵣ, where k,m,n,r,d and
Fatih Erduvan
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The extensibility of the Diophantine triple {2, b, c}
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple.
Adžaga Nikola +2 more
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Upper bounds for the number of solutions to quartic Thue equations [PDF]
, 2011 We will give upper bounds for the number of integral solutions to quartic Thue equations. Our main tool here is a logarithmic curve (x,y) that allows us to use the theory of linear forms in logarithms.
Akhtari, S.
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Extremal families of cubic Thue equations [PDF]
, 2014 We exactly determine the integral solutions to a previously untreated infinite family of cubic Thue equations of the form $F(x,y)=1$ with at least $5$ such solutions.
Bennett, Michael A., Ghadermarzi, Amir
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Sums of two ${s}$-units via frey-hellegouarch curves [PDF]
, 2015 In this paper, we develop a new method for finding all perfect powers which can be expressed as the sum of two rational S-units, where S is a finite set of primes. Our approach is based upon the modularity of Galois representations and, for the most part,
Bennett, Michael, Billerey, Nicolas
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Padovan and Perrin numbers of the form 7ᵗ-5ᶻ-3ʸ-2ˣ [PDF]
Notes on Number Theory and Discrete MathematicsConsider the Padovan sequence (pₙ)ₙ≥₀ given by pₙ₊₃=pₙ₊₁+pₙ with p₀=p₁=p₂=1. Its companion sequence, the Perrin sequence (℘ₙ)ₙ≥₀, follows the same recursive formula as the Padovan numbers, but with different initial values: p₀=3, p₁=0 and p₂=2.
Djamel Bellaouar +2 more
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Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms [PDF]
, 2007 We develop a theory of Tannakian Galois groups for t-motives and relate this to the theory of Frobenius semilinear difference equations. We show that the transcendence degree of the period matrix associated to a given t-motive is equal to the dimension ...
A. Tamagawa +31 more
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A kit for linear forms in three logarithms
Mathematics of Computation, 2023 We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds for linear forms in logarithms.
Mignotte, Maurice, Voutier, Paul
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Common values of two k-generalized Pell sequences [PDF]
Notes on Number Theory and Discrete MathematicsLet k≥2 and let (Pₙ⁽ᵏ⁾)ₙ≥₂₋ₖ be the k-generalized Pell sequence defined by Pₙ⁽ᵏ⁾=2Pₙ₋₁⁽ᵏ⁾+2Pₙ₋₂⁽ᵏ⁾+...+2Pₙ₋ₖ⁽ᵏ⁾ for n≥2 with initial conditions P₋₍ₖ₋₂₎⁽ᵏ⁾=P₋₍ₖ₋₃₎⁽ᵏ⁾=...=P₋₁⁽ᵏ⁾=P₀⁽ᵏ⁾=0, and P₁⁽ᵏ⁾=1.
Zafer Şiar +2 more
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