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By a famous theorem of Siegel [S], the number of integral points on an elliptic curve E over an algebraic number field K is finite. A conjecture of Lang and Demjanenko [L3] states that, for a… (More)
SummaryWe are concerned with families of dynamical systems which are related to generalized radix representations. The properties of these dynamical systems lead to new results on the… (More)
We give a survey on recent results concerning parametrized Thue equations. Moreover, we solve completely the family X(X − Y )(X − aY )(X − (a+ 1)Y )− Y 4 = ±1.
LetQ1, Q2∈Z[X, Y, Z] be two ternary quadratic forms andu1, u2∈Z. In this paper we consider the problem of solving the system of equations[formula]According to Mordell  the coprime solutions… (More)
In this paper we consider arithmetic progressions on Pell equations, i.e. integral solutions (X,Y) whose X-coordinates or Y-coordinates are in arithmetic progression.
We are concerned with families of dynamical systems which are related to generalized radix representations. The properties of these dynamical systems lead to new results on the characterization of… (More)
For a wide class of one-parameter families of Thue equations of arbitrary degree n [ges ]3 all solutions are determined if the parameter is sufficiently large. The result is based on the… (More)