Keywords and phrases: monogenity, power integral basis, trinomials, Thue equations.
Received: February 26, 2024; Revised: April 6, 2024; Accepted: April 8, 2024
How to cite this article: István Gaál, A note on the monogenity of some trinomials of type , JP Journal of Algebra, Number Theory and Applications 63(3) (2024), 265-279. http://dx.doi.org/10.17654/0972555524016
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References: [1] B. J. Birch and J. R. Merriman, Finiteness theorems for binary forms with given discriminant, Proc. London Math. Soc. 24 (1972), 385-394. [2] B. W. Char, K. O. Geddes, G. H. Gonnet, M. B. Monagan and S. M. Watt, eds., MAPLE, Reference Manual, Watcom Publications, Waterloo, Canada, 1988. [3] R. Dedekind, Über den Zusammenhang zwischen der Theorie der Ideale und der Theorie der höheren Kongruenzen, Göttingen Abhandlungen 23 (1878), 1-23. [4] L. El Fadil, On integral bases and monogeneity of pure sextic number fields with nonsquarefree coefficients, J. Number Theory 228 (2021), 375-389. [5] L. El Fadil and I. Gaál, Integral bases and monogenity of pure number fields with non-square free parameters up to degree 9, Tatra Mt. Math. Publ. 83 (2023), 61-86. [6] L. El Fadil and I. Gaál, On integral bases and monogenity of pure octic number fields with non-square free parameters, arXiv:2202.04417. [7] L. El Fadil and I. Gaál, On index divisors and monogenity of certain quartic number fields defined by arXiv:2204.03226. [8] I. Gaál, Diophantine equations and power integral bases, Theory and Algorithms, 2nd ed., Birkhäuser, Boston, 2019. [9] I. Gaál, On the monogenity of totally complex pure sextic fields, JP Journal of Algebra, Number Theory and Applications 60 (2023), 85-96. [10] I. Gaál, On the monogenity of totally complex pure octic fields, arXiv:2402.09293. [11] I. Gaál, A. Pethő and M. Pohst, On the resolution of index form equations in quartic number fields, J. Symbolic Comput. 16 (1993), 563-584. [12] I. Gaál, A. Pethő and M. Pohst, Simultaneous representation of integers by a pair of ternary quadratic forms - with an application to index form equations in quartic number fields, J. Number Theory 57 (1996), 90-104. [13] K. Győry, Sur les polynômes a coefficients entiers et de discriminant donne, III, Publ. Math. (Debrecen) 23 (1976), 141-165. [14] H. Hasse, Zahlentheorie, Akademie-Verlag, Berlin, 1963.
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