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For a positive integer $N$ and $\mathbb{A}$ a subset of $\mathbb{Q}$, let$\mathbb{A}$-$\mathcal{KS}(N)$ denote the set of$\alpha=\dfrac{\alpha_{1}}{\alpha_{2}}\in \mathbb{A}\setminus \{0,N\}$verifying $\alpha_{2}p-\alpha_{1}$ divides $\alpha_{2}N-\alpha_{1}$ for everyprime divisor $p$ of $N$. The set $\mathbb{A}$-$\mathcal{KS}(N)$ is called theset of Korselt bases of $N$ in $\mathbb{A}$ or simply the $\mathbb{A}$-Korseltset of $N$.  In this paper, we prove that for each squarefree composite number$N\in\mathbb{N}\setminus\{0,1\}$ the $\mathbb{Q}$-Korselt set of $N$ is finitewhere we provide an upper and lower bounds for each Korselt base of $N$ in$\mathbb{Q}$. Furthermore, we give a necessary and a sufficient condition forthe upper bound of a Korselt base to be reached.

Korselt Rational Bases and Sets