Prime powers in sums of terms of binary recurrence sequences

DOI10.1007/s00605-019-01282-wzbMath1447.11030arXiv1610.02774OpenAlexW2962798286MaRDI QIDQ2313398

Sudhansu Sekhar Rout, Eshita Mazumdar

Publication date: 19 July 2019

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.02774

zbMATH Keywords

linear forms in logarithmsreduction methodDiophantine equationsbalancing numbers

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Related Items (5)

Sums of \(S\)-units in sum of terms of recurrence sequences ⋮ \(S\)-parts of sums of terms of linear recurrence sequences ⋮ Cullen numbers in sums of terms of recurrence sequence ⋮ Linear combinations of prime powers in sums of terms of binary recurrence sequences ⋮ On the Zeckendorf representation of smooth numbers

Cites Work

• Diophantine equations concerning balancing and Lucas balancing numbers
• On the sum of powers of two consecutive Fibonacci numbers
• Powers of two as sums of three Fibonacci numbers
• Perfect powers in second order linear recurrences
• Effective resolution of Diophantine equations of the form \(u_n+u_m=w p_1^{z_1} \dotsm p_s^{z_s}\)
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• On a conjecture about repdigits in k-generalized Fibonacci sequences
• Linear combinations of prime powers in binary recurrence sequences
• Products of Prime Powers in Binary Recurrence Sequences Part I: The Hyperbolic Case, with an Application to the Generalized Ramanujan-Nagell Equation
• On the Diophantine equation $ax^{2t}+bx^ty+cy^2=d$ and pure powers in recurrence sequences.
• Perfect Pell Powers
• On The diophantine equationFn+F_m=2^a
• On Square Fibonacci Numbers
• Powers of two as sums of two k-Fibonacci numbers
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