Chapter 4.1, Problem 20MS

Natural right (S). Suppose r and s are any two natural numbers where r is bigger than s. Using the converse of the Pythagorean Theorem that appears at the end of Mindscape 22, show that the triangle having side lengths equal to ${\text{2rs, r}}^{\text{2}}{\text{-s}}^{\text{2}}{\text{, and r}}^{\text{2}}{\text{+ s}}^{\text{2}}$ is actually a right triangle. Are there infinitely many different right triangles having all sides of integer lengths?