# Borka Jadrijevič: A family of quartic Thue inequalities

## This is a joint work with Andrej Dujella.

We prove that the only primitive solutions of the Thue inequality

where is an integer, are , , , , , Solving Thue equations 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 (see [1,3]). 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 for which the equation has a solution. In particular, we use characterization in terms of continued fractions of of all fractions satisfying the inequality

## Bibliography

1
Andrej Dujella and Borka Jadrijevič.
A parametric family of quartic Thue equations.
Acta Arith., 101(2):159-170, 2002.

2
Andrej Dujella and Borka Jadrijevič.
A family of quartic Thue inequalities.
Acta Arith., 111(1):61-76, 2004.

3
Nikos Tzanakis.
Explicit solution of a class of quartic Thue equations.
Acta Arith., 64(3):271-283, 1993.

Please send comments and corrections to Thomas Klausner.