Naslov
A family of quartic Thue inequalities

Autori
Jadrijević, Borka

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Number Theoretic Algorithms and Related Topics / Drmota, M. ; Larcher, G. ; Tichy, R. ; Winkler, R. - Strobl : Technische Universitat Graz, 2004, 12-13

Skup
Workshop on Number Theoretic Algorithms and Related Topics

Mjesto i datum
Strobl, Austrija, 27.09.2004. - 01.10.2004

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Thue equations; Pellian equations

Sažetak
We prove that the only primitive solutions of the Thue inequality |x^4-4cx^y+(6c+2)x^2y^2+4cxy^3+y^4| <= 6c+4, where c>=4 is an integer, are (x, y)=(+-1, 0), (0, +-1), (1, +-1), (-1, +-1), (+-1, -+2), (+-2, +-1). Solving Thue equations F(x, y)=m of the special type, using the method of Tzanakis, reduces to solving the system of Pellian equations. The application of Tzanakis method for solving Thue equations has several advantages. We show that some additional advantages appear when one deals with corresponding Thue inequalities. Namely, the theory of continued fractions can be used in order to determine small values of m for which the equation F(x, y)=m has a solution. In particular, we use characterization in terms of continued fractions of alpha of all fractions a/b satisfying the inequality |alpha - a/b| < 2/b^2.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA