On binomial Thue equations and ternary equations with S-unit coefficients

• Autores: Andras Bazso
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 77, Fasc. 3-4, 2010, págs. 499-515
• Idioma: inglés
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• Resumen

  • Year: 2010 Vol.: 77 Fasc.: 3-4 Title: On binomial Thue equations and ternary equations with S-unit coe±cients Author(s): Andr¶as Bazs¶o In this paper we obtain some new results for a collection of equations of the form (2) Axn¡Byn = §1 resp. (3) Axn¡Byn = zm with m 2 f3; ng, where x, y, z, A, B, n are unknown nonzero integers such that n ¸ 3 is a prime and AB is composed of two ¯xed primes. We prove among other things that under certain conditions formulated in Section 2, equations (3) have no solutions with jxyj > 1, Ax, By and z coprime and n > 13 (cf. Theorems 2 to 4). Combining this with some other results and techniques, we establish a similar result for equations (2) (cf. Theorem 1).

    Address:

    Andr¶as Bazs¶o Institute of Mathematics Number Theory Research Group of the Hungarian Academy of Sciences University of Debrecen H-4010 Debrecen, P.O. Box 12 Hungary