Let N be a positive integer, A\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {A}}$$\end{document} be a nonempty subset of Q\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {Q}}$$\end{document} and α=α1α2∈A\{0,N}\documentclass[12pt]{minimal}
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\begin{document}$$\alpha =\dfrac{\alpha _{1}}{\alpha _{2}}\in {\mathbb {A}}{\setminus } \{0,N\}$$\end{document}. α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document} is called an N-Korselt base (equivalently N is said an α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}-Korselt number) if α2p-α1\documentclass[12pt]{minimal}
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\begin{document}$$\alpha _{2}p-\alpha _{1}$$\end{document} is a divisor of α2N-α1\documentclass[12pt]{minimal}
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\begin{document}$$\alpha _{2}N-\alpha _{1}$$\end{document} for every prime p dividing N. The set of all Korselt bases of N in A\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {A}}$$\end{document} is called the A\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {A}}$$\end{document}-Korselt set of N and is simply denoted by A\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {A}}$$\end{document}-KS(N)\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {KS}(N)$$\end{document}. Let p and q be two distinct prime numbers. In this paper, we study the Q\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {Q}}$$\end{document}-Korselt bases of pq, where we give in detail how to provide Q\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {Q}}$$\end{document}-KS(pq)\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {KS}(pq)$$\end{document}. Consequently, we finish the incomplete characterization of the Korselt set of pq over Z\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {Z}}$$\end{document} given in [4], by supplying the set Z\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {Z}}$$\end{document}-KS(pq)\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {KS}(pq)$$\end{document} when q<2p\documentclass[12pt]{minimal}
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\begin{document}$$q <2p$$\end{document}.
