CN-TST 2019 Problem 2

Fix a positive integer $n\geq 3$ . Does there exist infinitely many sets $S$ of positive integers $\lbrace a_1,a_2,\ldots, a_n$ , $b_1,b_2,\ldots,b_n\rbrace$ , such that $\gcd (a_1,a_2,\ldots, a_n$ , $b_1,b_2,\ldots,b_n)=1$ , $\lbrace a_i\rbrace _{i=1}^n$ , $\lbrace b_i\rbrace _{i=1}^n$ are arithmetic progressions, and $\prod_{i=1}^n a_i = \prod_{i=1}^n b_i$ ?