Problem - 166
Find all ordered pairs of integers $(x, y)$ that satisfy the equation $$\sqrt{y-\frac{1}{5}} + \sqrt{x-\frac{1}{5}} = \sqrt{5}$$
Without loss of generality, let's assume $x \le y$ which means $\sqrt{x-\frac{1}{5}} \le \sqrt{y-\frac{1}{5}}$. Therefore,
$$\sqrt{x-\frac{1}{5}}\le\frac{\sqrt{5}}{2}\implies x = 1 \implies y=2$$
Therefore all solutions are $\boxed{(1, 2), (2, 1)}$.