We reprove twice, in a simpler but as elementary way, a result by Hor\'ak and Skula (1985) who determined, among all sequences of integers defined by $$u_1=1,\quad u_2=R,\quad u_{n+2}=Pu_{n+1}-Qu_n$$ for some integers $P,Q,R$, those which satisfy the strong divisibility condition $$\forall i,j\in\mathbb N^*\quad u_i\land u_j=\left|u_{i\land j}\right|,$$ where $\land$ denotes the greatest common divisor.

翻译：我们两次以简单但基本的方式再次证明Hor\'ak和Skula(1985年)的结果。 Hor\'ak和Skula(1985年)在由美元=1,\quad u_2=R,\quad u_2=R,\quad u ⁇ n+2 ⁇ Pu ⁇ n+1} - Qu_n$,用于某些整数$P,Q,R$,那些满足强力差异条件的 $$_fall i,j\in\mathbb N ⁇ quad u_ileland u_j ⁇ left ⁇ u ⁇ i\land j ⁇ right}(美元,其中美元表示最常见的差价)。