The square terms in Lucas sequences

DOI10.1006/jnth.1996.0068zbMath0851.11011OpenAlexW1968837781WikidataQ56429718 ScholiaQ56429718MaRDI QIDQ1914032

Wayne L. McDaniel, Paulo Ribenboim

Publication date: 9 July 1996

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1996.0068

zbMATH Keywords

Fibonacci sequencesLucas sequencerecursive sequencessquare terms

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (22)

On the equation \(V_n=wx^2\mp 1\) ⋮ Lucas sequences whose 12th or 9th term is a square ⋮ On square classes in generalized Fibonacci sequences ⋮ THE SQUARE TERMS IN GENERALIZED LUCAS SEQUENCES ⋮ On squares in Lucas sequences ⋮ On the {L}ucas sequence equations {\(V_n(P,1)=wkx^2\)}, {\(w\in\{5,7\}\)} ⋮ On the Lucas sequence equations \(V_n=7\,\square \) and \(V_n=7V_m\,\square \) ⋮ Balancing and balancing-like numbers which are one away from perfect powers ⋮ Generalized Fibonacci numbers of the form \(wx^2 + 1\) ⋮ Sequences associated to elliptic curves with non-cyclic torsion subgroup ⋮ Squares in generalizations of Lucas sequences ⋮ Pythagorean triples containing generalized Lucas numbers ⋮ The terms of the form $7kx^{2}$ in the generalized Lucas sequence with parameters $P$ and $Q$ ⋮ Unnamed Item ⋮ Square-classes in Lucas sequences having odd parameters ⋮ An algorithm to determine the points with integral coordinates in certain elliptic curves ⋮ A new proof of a conjecture of Antoniadis ⋮ On square classes in generalized Lucas sequences ⋮ Generalized Fibonacci and Lucas numbers of the form 5x² ⋮ On the units and the class numbers of certain composita of two quadratic fields ⋮ Unnamed Item ⋮ A classification of (some) Pisot-cyclotomic numbers

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