The initial number of inhabitants of a city of more than $150$ inhabitants is a perfect square. With an increase of $1000$ inhabitants it becomes a perfect square plus a unit. After from another increase of $1000$ inhabitants it is again a perfect square. Determine the quantity of inhabitants that are initially in the city.
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist A2 day2
Tags: number theory, Perfect Squares, Perfect Square