Inhomogeneous Thue Equations

István Gaál
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István Gaál: University of Debrecen, Institute of Mathematics

Chapter Chapter 4 in Diophantine Equations and Power Integral Bases, 2019, pp 39-44 from Springer

Abstract: Abstract Let α be an algebraic integer of degree n ≥ 3, K = ℚ ( α ) $$K={\mathbb Q}(\alpha )$$ , and let 0 ≠ m ∈ ℤ $$0\neq m\in {\mathbb Z}$$ . In some applications for index form equations in sextic and octic fields (cf. Sects. 11.2.1 , 11.2.2 , and 14.2.3 ) we shall need to solve equations of type N K ∕ ℚ ( x + α y + λ ) = m in x , y ∈ ℤ , λ ∈ ℤ K , $$\displaystyle N_{K/{\mathbb Q}}(x+\alpha y +\lambda )=m \;\;\; \mathrm {in} \;\;\; x,y\in {\mathbb Z}, \lambda \in {\mathbb Z}_K, $$ where we assume that | λ | ¯

Date: 2019
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DOI: 10.1007/978-3-030-23865-0_4

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