MathDB

Prove that for any positive integer

k

, there exists an arithmetic sequence

\frac{a_1}{b_1}, \frac{a_2}{b_2}, \frac{a_3}{b_3}, ... ,\frac{a_k}{b_k}

of rational numbers, where

a_i, b_i

are relatively prime positive integers for each i \equal{} 1,2,...,k such that the positive integers

a_1, b_1, a_2, b_2, ..., a_k, b_k

are all distinct.

Problem Statement