Geodesic
On the arithmetic properties of a number $\sqrt[3]{2}+ \sqrt{3}$
Matematičeskoe obrazovanie, Tome 95 (2020) no. 3, pp. 2-7.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that this number is irrational and is an integer algebraic number of degree equal to six.
Keywords: irrational number, algebraic integer, power of an algebraic integer. 
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V. E. Volkov; V. B. Sherstyukov. On the arithmetic properties of a number $\sqrt[3]{2}+ \sqrt{3}$. Matematičeskoe obrazovanie, Tome 95 (2020) no. 3, pp. 2-7. http://geodesic.mathdoc.fr/item/MO_2020_95_3_a0/

[1] Sadovnichii V.A., Podkolzin A.S., Zadachi studencheskikh olimpiad po matematike, Nauka, M., 1978, 208 pp.

[2] Zhukov A., “Algebraicheskie i transtsendentnye chisla”, Kvant, 1998, no. 4, Kaleidoskop «Kvanta»

[3] Gelfond A.O., Transtsendentnye i algebraicheskie chisla, GITTL, M., 1952, 224 pp.

[4] Galochkin A.I., Nesterenko Yu.V., Shidlovskii A.B., Vvedenie v teoriyu chisel, Izd-vo Mosk. un-ta, M., 1984, 147 pp. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=759891'>759891</ext-link>

[5] Galieva L.I., Galyautdinov I.G., “Ob odnom klasse uravnenii, razreshimykh v radikalakh”, Izv. vuzov. Matem., 2011, no. 2, 22–30 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=2814818'>2814818</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1248.11079'>1248.11079</ext-link>