Let $A, B\subset \mathbb{Z}$ be two sets of integers. We say that $A,B$ are mutually repulsive if there exist positive integers $m,n$ and two sequences of integers $\alpha_1, \alpha_2, \dots, \alpha_n$ and $\beta_1, \beta_2, \dots, \beta_m$, for which there is a unique integer $x$ such that the number of its appearances in the sequence of sets $A+\alpha_1, A+\alpha_2, \dots, A+\alpha_n$ is different than the number of its appearances in the sequence of sets $B+\beta_1, \dots, B+\beta_m$. For a given quadruple of positive integers $(n_1,d_1, n_2, d_2)$, determine whether the sets \[A=\{d_1, 2d_1, \dots, n_1d_1\}\]\[B=\{d_2, 2d_2, \dots, n_2d_2\}\]are mutually repulsive. For a set $X\subset \mathbb{Z}$ and $c\in \mathbb{Z}$, we define $X+c=\{x+c\mid x\in X\}$.