A family of quartic Thue inequalities (CROSBI ID 497913)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa
Podaci o odgovornosti
Jadrijević, Borka
engleski
A family of quartic Thue inequalities
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.
Thue equations; Pellian equations
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Podaci o prilogu
12-13-x.
2004.
objavljeno
Podaci o matičnoj publikaciji
Number Theoretic Algorithms and Related Topics
Drmota, M. ; Larcher, G. ; Tichy, R. ; Winkler, R.
Strobl: Technische Universitat Graz
Podaci o skupu
Workshop on Number Theoretic Algorithms and Related Topics
predavanje
27.09.2004-01.10.2004
Strobl, Austrija