Question 4
Prove that for any positive integer $k$, there exists an arithmetic sequence $a_1/b_1,a_2/b_2,\ldots,a_k/b_k$ of rational numbers, where $a_i,b_i$ are relatively prime positive integers for each $i=1,2,\ldots,k$, such that the positive integers $a_1,b_1,a_2,b_2,\ldots,a_k,b_k$ are all distinct.