BG-MO 2001 Problem 4

Let $n \geq 2$ be a given integer. At any point $(i, j)$ with $i, j \in\mathbb{ Z}$ we write the remainder of $i+j$ modulo $n$ . Find all pairs $(a, b)$ of positive integers such that the rectangle with vertices $(0, 0)$ , $(a, 0)$ , $(a, b)$ , $(0, b)$ has the following properties:(i) the remainders $0, 1, \ldots , n-1$ written at its interior points appear the same number of times;(ii) the remainders $0, 1, \ldots , n -1$ written at its boundary points appear the same number of times.