Abstract
We consider the parametric family of sextic Thue equations $$x^6-2mx^5y-5(m+3)x^4y^2-20x^3y^3+5mx^2y^4+2(m+3)xy^5+y^6=\lambda$$ where $m\in\mathbb{Z}$ is an integer and $\lambda$ is a divisor of $27(m^2+3m+9)$. We show that the only solutions to the equations are the trivial ones with $xy(x+y)(x-y)(x+2y)(2x+y)=0$.
Citation
Akinari Hoshi. "On the simplest sextic fields and related Thue equations." Funct. Approx. Comment. Math. 47 (1) 35 - 49, September 2012. https://doi.org/10.7169/facm/2012.47.1.3
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