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Diophantine Equation Generated by the Maximal Subfield of a Circular Field
Russian Mathematics Pub Date : 2020-08-14 , DOI: 10.3103/s1066369x20070051
I. G. Galyautdinov , E. E. Lavrentyeva

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.

中文翻译:

圆场的最大子场生成的丢番图方程

使用字段\(L_9 = \ mathbb {Q}(2 \ cos(\ pi / 9)),\)的基础,形式\(N_ {L_9}(\ gamma)= f(x,y,z )\)被发现,并且丢番图方程\(f(x,y,z)= a \)被求解。类似的方案用于构造形式\(N_ {L_7}(\ gamma)= g(x,y,z)\)。求解丢番图方程\(g(x,y,z)= a \)
更新日期:2020-08-14
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