Sums of Tribonacci numbers close to powers of 2
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Jhon J. Bravo
Abstract
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 variant of the Baker-Davenport reduction method to determine all sums of two Tribonacci numbers that are close to powers of 2, based on a notion of closeness introduced by Chern and Cui. Specifically, it determines all nonnegative integer solutions (n, m, a) to the Diophantine inequality ∣Tn+Tm –2a| < 2a/2. This work extends a previous result of Hasanalizade who found all sums of two Fibonacci numbers close to a power of 2.
Funding statement: This work was supported in part by Project VRI ID 6115 (Universidad del Cauca).
Acknowledgement
The author thanks the reviewer for comments which improved the quality of this paper. This work was supported in part by Project VRI ID 6115 (Universidad del Cauca).
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(Communicated by István Gaál)
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Artikel in diesem Heft
- Copies of monomorphic structures
- Endomorphism kernel property for extraspecial and special groups
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- Multiplicative functions k-additive on hexagonal numbers
- Monogenic even cyclic sextic polynomials
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- Degree of independence in non-archimedean fields
- Remarks on some one-ended groups
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- Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
- Radius estimates for functions in the class 𝒰r(λ)
- Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
- More q-congruences from Singh’s quadratic transformation
- Stability and controllability of cycled dynamical systems
- Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
- Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
- Coincidence points via tri-simulation functions with an application in integral equations
- On Fong-Tsui conjecture and binormality of operators
- Riemannian maps of CR-submanifolds of Kaehler manifolds
- On structural numbers of topological spaces
- The κ-Fréchet-Urysohn property for Cp(X) is equivalent to baireness of B1(X)
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