Theory and ExamplesPythagorean triples A triple of
Chapter 10, Problem 103E(choose chapter or problem)
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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