Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 5 - Section 5.4 - The Pythagorean Theorem - Exercises - Page 242: 42


Pythagorean triple

Work Step by Step

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.
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