[ Pythagorean Theorem (direct and inverse). ] [ Examples and counterexamples. Constructions ]

Is there a right triangle in which the lengths of two sides are integers, and the length of the third side is $\sqrt{2016}$?
Consider, for example, a right-angled triangle with legs $\sqrt{2016}$ and 3. Its hypotenuse is equal to $\sqrt{2016+9}=\sqrt{2025}=45$.

## Answer

It exists.