Calculating “Small” Solutions of Relative Thue Equations

@article{Gal2015CalculatingS,
  title={Calculating “Small” Solutions of Relative Thue Equations},
  author={Istv{\'a}n Ga{\'a}l},
  journal={Experimental Mathematics},
  year={2015},
  volume={24},
  pages={142 - 149}
}
  • I. Gaál
  • Published 25 March 2015
  • Mathematics, Computer Science
  • Experimental Mathematics
Diophantine equations can often be reduced to various types of classical Thue equations. These equations usually have only very small solutions. On the other hand, to compute all solutions (i.e., to prove the nonexistence of large solutions) is a time-consuming procedure. Therefore, it is useful to have a fast algorithm to calculate the “small” solutions, especially if “small” means less than, e.g., 10100. Such an algorithm was constructed by A. Pethö in 1987 based on continued fractions. In… Expand
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  • I. Gaál
  • Physics
  • Diophantine Equations and Power Integral Bases
  • 2019
Let M ⊂ K be algebraic number fields, and let K = M(α) with an algebraic integer α. Let \(0\neq \mu \in {\mathbb Z}_M\). Consider the relative Thue equation $$\displaystyle N_{K/M}(X-\alpha Y)=\muExpand

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