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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Kazan Federal University
2024-07-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/66 |
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| Summary: | 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. |
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| ISSN: | 2541-7746 2500-2198 |