Multiplicative Dependent Pairs in the Sequence of Padovan Numbers
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Mitashree Behera
ABSTRACT
The Padovan sequence {Pn}n≥0 is a ternary recurrent sequence defined recursively by the relation Pn = Pn–2 + Pn–3 with initials P0 = P1 = P2 = 1. In this note, we search all pairs of multiplicative dependent vectors whose coordinates are Padovan numbers. For this purpose, we apply Matveev’s theorem to find the lower bounds of the non-zero linear forms in logarithms. Techniques involving the LLL algorithm and the theory of continued fraction are utilized to reduce the bounds.
Acknowledgement
We would like to thank the anonymous referees for their valuable comments and suggestions in order to improve the quality of this article.
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© 2023 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Remembering Professor Štefan Znám, 9.2.1936–17.7.1993
- Chordal and Perfect Zero-Divisor Graphs of Posets and Applications to Graphs Associated with Algebraic Structures
- Enlargements of Quantales
- Multiplicative Dependent Pairs in the Sequence of Padovan Numbers
- Dirichlet Series with Periodic Coefficients, Riemann’s Functional Equation, and Real Zeros of Dirichlet L-Functions
- On the Rational Parametric Solution of Diagonal Quartic Varieties
- Theory of Certain Non-Univalent Analytic Functions
- Initial Coefficients and Fekete-Szegő Inequalities for Functions Related to van der Pol Numbers (VPN)
- A Conjecture on H3(1) for Certain Starlike Functions
- Coefficient Problems of Quasi-Convex Mappings of Type B on the Unit Ball in Complex Banach Spaces
- Complete Monotonicity and Inequalities Involving the k-Gamma and k-Polygamma Functions
- Study of Oscillation Criteria of Odd-Order Differential Equations with Mixed Neutral Terms
- On a System of Difference Equations Defined by the Product of Separable Homogeneous Functions
- On the Existence of Bi-Lipschitz Equivalent Metrics in Semimetric Spaces
- The Lehmann Type II Teissier Distribution
- Asymptotic Predictive Inference of Negative Lower Tail Index Distributions
- On Numerical Problems in Computing Life Annuities Based on the Makeham–Beard Law
- The Rational Zero-Divisor Cup-Length of Oriented Partial Flag Manifolds
