On the {L}ucas sequence equations {\(V_n(P,1)=wkx^2\)}, {\(w\in\{5,7\}\)}

DOI10.1007/s10998-016-0130-7zbMath1389.11037OpenAlexW2340554875MaRDI QIDQ1677556

Olcay Karaatlı

Publication date: 10 November 2017

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

Full work available at URL: https://doi.org/10.1007/s10998-016-0130-7

zbMATH Keywords

congruencesJacobi symbolgeneralized Fibonacci numbersgeneralized Lucas numbers

Mathematics Subject Classification ID

Recurrences (11B37) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Sequences (mod (m)) (11B50)

Uses Software

• Magma

Cites Work

• The Magma algebra system. I: The user language
• On the Lucas sequence equations \(V_n=7\,\square \) and \(V_n=7V_m\,\square \)
• The square terms in Lucas sequences
• Squares in some recurrent sequences
• On the Equations U_{n}=5□ and V_{n}=5□
• GENERALIZED FIBONACCI AND LUCAS NUMBERS OF THE FORM wx²AND wx²∓ 1
• 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
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