English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $m\geq -1$ be an integer. We give a correspondence between integersolutions to the parametric family of cubic Thue equations \[X^3-mX^2Y-(m+3)XY^2-Y^3=\lambda \] where $\lambda>0$ is a divisor of $m^2+3m+9$and isomorphism classes of the simplest cubic fields. By the correspondence andR. Okazaki's result, we determine the exactly 66 non-trivial solutions to theThue equations for positive divisors $\lambda$ of $m^2+3m+9$. As a consequence,we obtain another proof of Okazaki's theorem which asserts that the simplestcubic fields are non-isomorphic to each other except for$m=-1,0,1,2,3,5,12,54,66,1259,2389$.

On correspondence between solutions of a family of cubic Thue equations and isomorphism classes of the simplest cubic fields