Studying the divisibility of power LCM matrics by power GCD matrices on gcd-closed sets

Jianrong Zhao, Chenxu Wang, Yu Fu

Let $S=\{x_1,\dots ,x_n\}$ be a gcd-closed set (i.e. $(x_i,x_j)\in S$ for all $1\le i,j\le n$). In 2002, Hong proposed the divisibility problem of characterizing all gcd-closed s…