Generalized Fibonacci numbers of the form \(wx^2 + 1\)

DOI10.1007/s10998-016-0133-4zbMath1399.11044OpenAlexW2412354799MaRDI QIDQ1701404

Refik Keskin, Ümmügülsüm Öğüt

Publication date: 22 February 2018

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10998-016-0133-4

zbMATH Keywords

congruencesDiophantine equationgeneralized Fibonacci numbersgeneralized Lucas numbers

Mathematics Subject Classification ID

Recurrences (11B37) Higher degree equations; Fermat's equation (11D41) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Sequences (mod (m)) (11B50) Sequences and sets (11B99)

Related Items (2)

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Uses Software

• Magma

Cites Work

• Solutions of some quadratic Diophantine equations
• Fibonacci numbers at most one away from a perfect power
• Almost powers in the Lucas sequence
• The Magma algebra system. I: The user language
• The square terms in Lucas sequences
• Positive integer solutions of the Diophantine equation \(x^2-L_nxy+(-1)^ny^2=\pm 5^ r\)
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• Squares in some recurrent sequences
• GENERALIZED FIBONACCI AND LUCAS NUMBERS OF THE FORM wx²AND wx²∓ 1
• On integral points on biquadratic curves and near-multiples of squares in Lucas sequences
• Generalized Fibonacci and Lucas Sequences and Rootfinding Methods
• THE SQUARE TERMS IN GENERALIZED LUCAS SEQUENCES
• GENERALIZED LUCAS NUMBERS OF THE FORM 5kx²AND 7kx²
• The Fibonacci Numbers: Exposed
• Generalized Fibonacci and Lucas numbers of the form 5x²
• Shifted powers in binary recurrence sequences
• The Diophantine Equation $3x^4-2y^2=1$.
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