Simplest Cubic Fields

Let $Q(α)$ be the simplest cubic field, it is known that $Q(α)$ can be generated by adjoining a root of the irreducible equation $x^{3}-kx^{2}+(k-3)x+1=0$, where $k$ belongs to $Q$. In this paper we have established a relationship between $α$, $α'$ and $k,k'$ where $α$ is a root of the equation $x^{3}-kx^{2}+(k-3)x+1=0$ and $α'$ is a root of the same equation with $k$ replaced by $k'$ and $Q(α)=Q(α')$.

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