Diophantine Equation Generated by the Subfield of a Circular Field
Two forms f (x, y, z) and g(x, y, z) of degree 3 were constructed, with their values being the norms of numbers in the subfields of degree 3 of the circular fields K13 and K19 , respectively. Using the decomposition law in a circular field, Diophantine equations f (x, y, z) = a and g(x, y, z) = b , whe...
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Kazan Federal University
2024-07-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/66 |
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| author | I. G. Galyautdinov E. E. Lavrentyeva |
| author_facet | I. G. Galyautdinov E. E. Lavrentyeva |
| author_sort | I. G. Galyautdinov |
| collection | DOAJ |
| description | Two forms f (x, y, z) and g(x, y, z) of degree 3 were constructed, with their values being the norms of numbers in the subfields of degree 3 of the circular fields K13 and K19 , respectively. Using the decomposition law in a circular field, Diophantine equations f (x, y, z) = a and g(x, y, z) = b , where a, b ∈ Z, a 6= 0, b 6= 0 were solved. The assertions that, based on the canonical decomposition of the numbers a and b into prime factors, make it possible to determine whether the equations f (x, y, z) = a and g(x, y, z) = b have solutions were proved. |
| format | Article |
| id | doaj-art-0fb8a9f010f740ffa697845423bbc71b |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-0fb8a9f010f740ffa697845423bbc71b2025-02-03T12:00:35ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982024-07-01166214716110.26907/2541-7746.2024.2.147-16140Diophantine Equation Generated by the Subfield of a Circular FieldI. G. Galyautdinov0E. E. Lavrentyeva1Kazan Federal UniversityKazan Federal UniversityTwo forms f (x, y, z) and g(x, y, z) of degree 3 were constructed, with their values being the norms of numbers in the subfields of degree 3 of the circular fields K13 and K19 , respectively. Using the decomposition law in a circular field, Diophantine equations f (x, y, z) = a and g(x, y, z) = b , where a, b ∈ Z, a 6= 0, b 6= 0 were solved. The assertions that, based on the canonical decomposition of the numbers a and b into prime factors, make it possible to determine whether the equations f (x, y, z) = a and g(x, y, z) = b have solutions were proved.https://uzakufismat.elpub.ru/jour/article/view/66algebraic integergalois groupnorm of algebraic numberprincipal idealfundamental basisdecomposition law in circular fielddiophantine equation |
| spellingShingle | I. G. Galyautdinov E. E. Lavrentyeva Diophantine Equation Generated by the Subfield of a Circular Field Учёные записки Казанского университета: Серия Физико-математические науки algebraic integer galois group norm of algebraic number principal ideal fundamental basis decomposition law in circular field diophantine equation |
| title | Diophantine Equation Generated by the Subfield of a Circular Field |
| title_full | Diophantine Equation Generated by the Subfield of a Circular Field |
| title_fullStr | Diophantine Equation Generated by the Subfield of a Circular Field |
| title_full_unstemmed | Diophantine Equation Generated by the Subfield of a Circular Field |
| title_short | Diophantine Equation Generated by the Subfield of a Circular Field |
| title_sort | diophantine equation generated by the subfield of a circular field |
| topic | algebraic integer galois group norm of algebraic number principal ideal fundamental basis decomposition law in circular field diophantine equation |
| url | https://uzakufismat.elpub.ru/jour/article/view/66 |
| work_keys_str_mv | AT iggalyautdinov diophantineequationgeneratedbythesubfieldofacircularfield AT eelavrentyeva diophantineequationgeneratedbythesubfieldofacircularfield |