CMO 1987 Problem 5

For every positive integer $n$ show that $$[\sqrt{4n + 1}] = [\sqrt{4n + 2}] = [\sqrt{4n + 3}] = [\sqrt{n} + \sqrt{n + 1}]$$ where $[x]$ is the greatest integer less than or equal to $x$ (for example $[2.3] = 2$ , $[\pi] = 3$ , $[5] = 5$ ).