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# The Hermite-Joubert Problem and a Conjecture of Brassil-Reichstein

Published:2018-03-20

• Khoa Dang Nguyen,
Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4
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## Abstract

show that Hermite's theorem fails for every integer $n$ of the form $3^{k_1}+3^{k_2}+3^{k_3}$ with integers $k_1\gt k_2\gt k_3\geq 0$. This confirms a conjecture of Brassil and Reichstein. We also obtain new results for the relative Hermite-Joubert problem over a finitely generated field of characteristic $0$.
 Keywords: Hermite-Joubert problem, Brassil-Reichstein conjecture, diophantine equation