Complete solutions of a family of quartic Thue and index form equations

Maurice Mignotte, Attila Pethö, Ralf Roth

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

Continuing the recent work of the second author, we prove that the diophantine equation fα (x, y) = x4 - αx3y - x2y2 + αxy3 + y4 = 1 for /α/ ≥ 3 has exactly 12 solutions except when |α| = 4. when it has 16 solutions. If α = α(α) denotes one of the zeros of fα(xx, 1), then for lαl ≥ 4 we also find all γ ∈ ℤ[α] with ℤ[γ] = ℤ[α].

Original languageEnglish
Pages (from-to)341-354
Number of pages14
JournalMathematics of Computation
Volume65
Issue number213
DOIs
Publication statusPublished - Jan 1 1996

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Keywords

  • Distributed computation
  • Index form equation
  • Linear forms in the logarithms of algebraic numbers
  • Thue equation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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