| Abstract [eng] |
The 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 αβγ=1. This work extends the investigation of product-feasible triplets started by Drungilas, Dubickas and Smyth. More precisely, for all but eight positive integer triplets (a, b, c) with a<=b<=c and b<=7, we decide whether it is product-feasible. Moreover, a result related to reducibilty of so called compositum-feasible triplets is obtained. The triplet (a,b,c) of positive integers is said to be compositum-feasible if there exist number fields K and L of degree a and b respectively such that the degree of the compositum KL equals c. We have showed that triplets of the form (n, n, n(n-1)), n\geq 2, cannot be written as (n, n, n(n-1))=(aa', bb', cc'), where (a, b, c) and (a', b', c') are compositum-feasible triplets both different from (1, 1, 1). |
