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
 1

Andrej Dujella and Borka Jadrijevič.
A parametric family of quartic Thue equations.
Acta Arith., 101(2):159170, 2002.
 2

Andrej Dujella and Borka Jadrijevič.
A family of quartic Thue inequalities.
Acta Arith., 111(1):6176, 2004.
 3

Nikos Tzanakis.
Explicit solution of a class of quartic Thue equations.
Acta Arith., 64(3):271283, 1993.
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