Binomial Thue equations, ternary equations, and power values of polynomials

K. Gyory, A. Pintér

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We explicitly solve the equation Axn-Byn = ±1 and, along the way, we obtain new results for a collection of equations Axn-Byn = zm with m ∈ {3, n}, where x, y, z, A, B, and n are unknown nonzero integers such that n ≤ 3, AB = pαqβ with nonnegative integers α and β and with primes 2 ≤ p < q < 30. The proofs require a combination of several powerful methods, including the modular approach, recent lower bounds for linear forms in logarithms, somewhat involved local considerations, and computational techniques for solving Thue equations of low degree.

Original languageEnglish
Pages (from-to)61-77
Number of pages17
JournalFundamental and Applied Mathematics
Volume16
Issue number5
Publication statusPublished - Dec 1 2010

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology
  • Applied Mathematics

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