Let f(x) be a trinomial (i.e., an irreducible polynomial with three terms), denote by a a root of f(x). f(x) is called monogenic, if α generates a power integral basis in

There is an extensive literature of monogenic trinomials. A natural question is to ask if K has power integral bases, different from the one generated by α. In the present paper we consider this question in a special infinite parametric family of trinomials. Our purpose is to describe all generators of power integral bases in the number fields generated by the roots of the trinomials.

monogenity, power integral basis, trinomials, sextic fields, calculating the solutions, relative Thue equations.

Received: April 23, 2021; Accepted: May 12, 2021; Published: June 28, 2021

How to cite this article: István Gaál, An experiment on the monogenity of a family of trinomials, JP Journal of Algebra, Number Theory and Applications 51(1) (2021), 97-111. DOI: 10.17654/NT051010097

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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