Problem

Source: Paraguayan National Olympiad 2011, Level 3, Problem 3

Tags: number theory proposed, number theory



If number $\overline{aaaa}$ is divided by $\overline{bb}$, the quotient is a number between $140$ and $160$ inclusively, and the remainder is equal to $\overline{(a-b)(a-b)}$. Find all pairs of positive integers $(a,b)$ that satisfy this.