Diophantine Equation Generated by the Subfield of a Circular Field
https://doi.org/10.26907/2541-7746.2024.2.147-161
Abstract
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.
About the Authors
I. G. Galyautdinov
Kazan Federal University
Russian Federation
Russian Federation
Kazan, 420008
E. E. Lavrentyeva
Kazan Federal University
Russian Federation
Russian Federation
Kazan, 420008
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Review
For citations:
Galyautdinov I.G., Lavrentyeva E.E. Diophantine Equation Generated by the Subfield of a Circular Field. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2024;166(2):147-161. (In Russ.) https://doi.org/10.26907/2541-7746.2024.2.147-161
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