Theory and ExamplesPythagorean triples A triple of

Chapter 10, Problem 103E

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Problem 103E

Theory and Examples

Pythagorean triples A triple of positive integers a, b, and c is called a Pythagorean triple if a2 + b2 = c2. Let a be an odd positive integer and let

be, respectively, the integer floor and ceiling for a2 /2.

a. Show that a2 + b2 = c2 (Hint : Let a = 2n + 1 and express b and c in terms of n.)

b. By direct calculation, or by appealing to the accompanying figure, find

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