## Elementary Geometry for College Students (6th Edition)

A Pythagorean triple occurs when all three numbers given in the Pythagorean theorem are whole numbers. Thus, we have: $a^2 + b^2 = c^2$ We substitute in the n to have: $a^2n^2 + b^2n^2 = c^2n^2 \\ n^2(a^2 + b^2 = c^2)$ Since an integer times another integer is an integer, it follows that this is also a Pythagorean triple.