Geodesic
The Hermite–Joubert Problem and a Conjecture of Brassil and Reichstein
Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 169-177

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DOI

We show that Hermite’s theorem fails for every integer $n$ of the form $3^{k_{1}}+3^{k_{2}}+3^{k_{3}}$ with integers $k_{1}>k_{2}>k_{3}\geqslant 0$. 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.
DOI : 10.4153/CMB-2018-004-0
Mots-clés : Hermite–Joubert problem, Brassil–Reichstein conjecture, diophantine equation 
Nguyen, Khoa Dang. The Hermite–Joubert Problem and a Conjecture of Brassil and Reichstein. Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 169-177. doi: 10.4153/CMB-2018-004-0
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     title = {The {Hermite{\textendash}Joubert} {Problem} and a {Conjecture} of {Brassil} and {Reichstein}},
     journal = {Canadian mathematical bulletin},
     pages = {169--177},
     year = {2019},
     volume = {62},
     number = {1},
     doi = {10.4153/CMB-2018-004-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-004-0/}
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