Question 85
Let $d$ be a positive divisor of a positive integer $m$ and $(a_{l}),(b_{l})$ two arithmetic sequences of positive integers. It is given that $\operatorname{gcd}(a_{i}, b_{j})=1$ and $\operatorname{gcd}(a_{k}, b_{n})= m$ for some positive integers $i, j, k$, and $n$. Prove that there exist positive integers $t$ and $s$ such that $\operatorname{gcd}(a_{t}, b_{s})=d$.