Diophantine Equation Generated by the Maximal Subfield of a Circular Field

Galyautdinov, I. G.; Lavrentyeva, E. E.

doi:10.3103/s1066369x20070051

Russ Math.

2020

DOI: 10.3103/s1066369x20070051

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Diophantine Equation Generated by the Maximal Subfield of a Circular Field

I. G. Galyautdinov

E. E. Lavrentyeva

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2024

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Diophantine Equation Generated by the Subﬁeld of a Circular Field

Galyautdinov,

Lavrentyeva

2024

jour

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Построены две формы f (x, y, z) и g(x, y, z) третьей степени, значения которых являются нормами чисел подполей степени три круговых полей K13 и K19 соответственно. С использованием закона разложения в круговом поле решены диофантовы уравнения f (x, y, z) = a и g(x, y, z) = b, a, b ∈ Z, a 6 = 0, b 6 = 0 . Доказаны утверждения, позволяющие по каноническому разложению на простые множители чисел a и b определить, имеют ли решения собственно уравнения f (x, y, z) = a, g(x, y, z) = b .

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Diophantine Equation Generated by the Subﬁeld of a Circular Field

Galyautdinov,

Lavrentyeva

2024

jour

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Diophantine Equation Generated by the Maximal Subfield of a Circular Field

Cited by 1 publication

References 7 publications

Diophantine Equation Generated by the Subﬁeld of a Circular Field

Diophantine Equation Generated by the Subﬁeld of a Circular Field

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