On the Degree of Product of Two Algebraic Numbers

Lukas Maciulevičius ()
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Lukas Maciulevičius: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania

Mathematics, 2023, vol. 11, issue 9, 1-10

Abstract: A triplet ( a , b , c ) of positive integers is said to be product-feasible if there exist algebraic numbers α , β and γ of degrees (over Q ) a , b and c , respectively, such that α β γ = 1 . This work extends the investigation of product-feasible triplets started by Drungilas, Dubickas and Smyth. More precisely, for all but five positive integer triplets ( a , b , c ) with a ≤ b ≤ c and b ≤ 7 , we decide whether it is product-feasible. Moreover, in the Appendix we give an infinite family or irreducible compositum-feasible triplets and propose a problem to find all such triplets.

Keywords: algebraic numbers; product-feasible; compositum-feasible; subgroups of symmetric groups (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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