Binomial Thue equations, ternary equations and power values of polynomials

K. Gyory, Á Pintér

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We explicitly solve the equation Ax n - By n = ±1 and, along the way, we obtain new results for a collection of equations Ax n - By n = z m with m ∈ {3, n}, where x, y, z, A, B, and n are unknown nonzero integers such that n ≥ 3, AB = p αq β with nonnegative integers α and β and with primes 2 ≤ p < q < 30. The proofs depend on 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)569-580
Number of pages12
JournalJournal of Mathematical Sciences
Volume180
Issue number5
DOIs
Publication statusPublished - Feb 1 2012

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ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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