On degrees of three algebraic numbers with zero sum or unit product

@inproceedings{Drungilas2016OnDO,
  title={On degrees of three algebraic numbers with zero sum or unit product},
  author={Paulius Drungilas and Artūras Dubickas},
  year={2016}
}
Let α, β and γ be algebraic numbers of respective degrees a, b and c over Q such that α + β + γ = 0. We prove that there exist algebraic numbers α1, β1 and γ1 of the same respective degrees a, b and c over Q such that α1β1γ1 = 1. This proves a previously formulated conjecture. We also investigate the problem of describing the set of triplets (a, b, c) ∈ N for which there exist finite field extensions K/k and L/k (of a fixed field k) of degrees a and b, respectively, such that the degree of the… 
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