Pythagorean triples A triple of positive integers a, b, and c is called a Pythagorean triple if a? + b? = c?. Let a be an odd positive integer and let and be, respectively, the integer floor and ceiling for a/2. a a. Show that a? + b = c?. (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 a? lim a 00

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