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On the Degree of Product of Two Algebraic Numbers

Author

Listed:
  • Lukas Maciulevičius

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

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.

Suggested Citation

  • Lukas Maciulevičius, 2023. "On the Degree of Product of Two Algebraic Numbers," Mathematics, MDPI, vol. 11(9), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2131-:d:1138138
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