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

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) AxniByn = §1 resp. (3) AxniByn = 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