Binomial Thue equations, ternary equations and power values of polynomials

K. Gyory, Á Pintér

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5 Citations (Scopus)


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
Issue number5
Publication statusPublished - Feb 1 2012


ASJC Scopus subject areas

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

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