The polynomial Pell equation

DOI10.1007/s00017-004-0214-7zbMath1077.11020OpenAlexW2107744288MaRDI QIDQ2566615

Jörn Steuding, Arturas Dubickas

Publication date: 26 September 2005

Published in: Elemente der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00017-004-0214-7

zbMATH Keywords

\(abc\)-conjecturePell equationspolynomial Diophantine equations

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09)

Related Items

A note on the use of Rédei polynomials for solving the polynomial Pell equation and its generalization to higher degrees ⋮ Unnamed Item ⋮ Properties of solutions to Pell’s equation over the polynomial ring ⋮ Simple superelliptic Lie algebras ⋮ ON THE EQUATION f(g(x))=f(x)h^m(x) FOR COMPOSITE POLYNOMIALS ⋮ Certain families of polynomials arising in the study of hyperelliptic Lie algebras ⋮ On admissible entire solutions of Pell type functional equation \(f^2 + ag ^2 = 1\) ⋮ Families of orthogonal Laurent polynomials, hyperelliptic lie algebras and elliptic integrals ⋮ Markov and Lagrange spectra for Laurent series in $1/T$ with rational coefficients

Cites Work

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• The \(abc\)-conjecture
• Pell equations for polynomials
• An alternate proof of Mason's theorem
• Quasi-elliptic integrals and periodic continued fractions
• Genus one curves defined by separated variable polynomials and a polynomial Pell equation
• POLYNOMIAL IDENTITIES AND HAUPTMODULN
• Polynomial Pell's Equations
• POLYNOMIAL SOLUTIONS OF PELL'S EQUATION AND FUNDAMENTAL UNITS IN REAL QUADRATIC FIELDS
• Polynomial Pell’s equation
• Pell's equation

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