Arithmetic properties of polynomial solutions of the Diophantine equation \(P(x)x^{n+1} + Q(x)(x + 1)^{n+1} = 1\)

DOI10.1007/s10998-020-00376-5OpenAlexW3159224994MaRDI QIDQ2077900

Karl Dilcher, Maciej Ulas

Publication date: 22 February 2022

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

Full work available at URL: https://arxiv.org/abs/1909.11222

zbMATH Keywords

generating functiondiscriminantresultantrecurrence sequencepolynomial diophantine equation

Mathematics Subject Classification ID

Polynomials in general fields (irreducibility, etc.) (12E05) Special polynomials in general fields (12E10) Linear Diophantine equations (11D04)

Cites Work

• Discriminants of polynomials related to Chebyshev polynomials: the ``Mutt and Jeff syndrome
• Resultants of Chebyshev polynomials
• Diophantine sets over polynomial rings
• Discriminants of Chebyshev-like polynomials and their generating functions
• POLYNOMIAL IDENTITIES AND HAUPTMODULN
• Polynomial Pell's Equations
• The Diophantine Problem for Polynomial Rings and Fields of Rational Functions
• Resultants and discriminants of Chebyshev and related polynomials
• On the interval containing at least one prime number
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