On squares in certain Lucas sequences

DOI10.5802/JTNB.97zbMath0795.11007OpenAlexW2012851991MaRDI QIDQ1320519

Attila Pethoe, Maurice Mignotte

Publication date: 16 May 1994

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_1993__5_2_333_0

zbMATH Keywords

Lucas sequencesquare values

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Higher degree equations; Fermat's equation (11D41) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (8)

THE SQUARE TERMS IN GENERALIZED LUCAS SEQUENCES ⋮ On solutions of the simultaneous {P}ell equations {\(x^2-(a^2-1)y^2=1\)} and {\(y^2-pz^2=1\)} ⋮ On the Mordell-Weil group of elliptic curves induced by families of Diophantine triples ⋮ On the determination of solutions of simultaneous Pell equations \(x^2 - (a^2 - 1) y^2 = y^2 - pz^2 = 1\) ⋮ THE ADDITIVE S-UNIT STRUCTURE OF QUADRATIC FIELDS ⋮ Integral points on the elliptic curve \(E_{ pq }\): \(y^2 = x^3 + ( pq - 12) x - 2( pq - 8)\) ⋮ An algorithm to determine the points with integral coordinates in certain elliptic curves ⋮ Explicit formula for the solution of simultaneous Pell equations 𝑥²-(𝑎²-1)𝑦²=1, 𝑦²-𝑏𝑧²=1

Cites Work

• The diophantine equation \(x^ 4 - kx^ 2 y^ 2 + y^ 4 = 1\)
• Linear forms in two logarithms and Schneider's method (III)
• Minorations de Combinaisons Linéaires de Logarithmes de Nombres Algébriques
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²
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