Complete solutions to families of quartic thue equations

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

Using a method due to E. Thomas, we prove that if a> 9.9 1027then the Diophantine equations. x4-x3y-x2y2+ axy3+y4=1 and x4-ax3y-3x2y2+ axy3+y4=±1 have exactly twelve solutions, namely (x, y) = (0, ±1), (±1, 0), (±1, ±1), (+-1, ±1), (±a, ±l), (±\, Ta) and eight solutions, (x, y) = (0, ±1), (±1, 0), (±1, ±1), (±1, Tl), respectively.

Original languageEnglish
Pages (from-to)777-798
Number of pages22
JournalMathematics of Computation
Volume57
Issue number196
DOIs
Publication statusPublished - 1991

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Thue Equations
Diophantine equation
Quartic
Family

Keywords

  • Linear forms in the logarithms of algebraic numbers
  • Thue equation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Cite this

Complete solutions to families of quartic thue equations. / Pethő, A.

In: Mathematics of Computation, Vol. 57, No. 196, 1991, p. 777-798.

Research output: Contribution to journalArticle

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