| Abstract [eng] |
A triplet (Formula presented.) of positive integers is said to be product-feasible if there exist algebraic numbers (Formula presented.), (Formula presented.) and (Formula presented.) of degrees (over (Formula presented.)) a, b and c, respectively, such that (Formula presented.). This work extends the investigation of product-feasible triplets started by Drungilas, Dubickas and Smyth. More precisely, for all but five positive integer triplets (Formula presented.) with (Formula presented.) and (Formula presented.), 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. |
