Geodesic
Diophantine equation generated by the maximal subfield of a circular field
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2020), pp. 45-55

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Using the fundamental basis of the field $L_9=\mathbb{Q} (2\cos(\pi/9))$, the form $N_{L_9}(\gamma)=f(x, y, z)$ is found and the Diophantine equation $f(x,y,z)=a$ is solved. A similar scheme is used to construct the form $N_{L_7}(\gamma)=g(x,y,z)$. The Diophantine equation $g (x, y, z)=a$ is solved.
Keywords: algebraic integer number, fundamental basis of an algebraic number field, norm of algebraic number, basic units of an algebraic field
Mots-clés : diophantine equation. 
@article{IVM_2020_7_a4,
     author = {I. G. Galyautdinov and E. E. Lavrentyeva},
     title = {Diophantine equation generated by the maximal subfield of a circular field},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {45--55},
     publisher = {mathdoc},
     number = {7},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_7_a4/}
}
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I. G. Galyautdinov; E. E. Lavrentyeva. Diophantine equation generated by the maximal subfield of a circular field. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2020), pp. 45-55. http://geodesic.mathdoc.fr/item/IVM_2020_7_a4/