A triple of positive integers a, b, and c is called a Pythagorean triple if a 2 b 2 c 2 Let a be an odd positive integer and let be, respectively, the integer floor and ceiling for a 2 2 a Show that a 2 b 2 c 2 b By direct calculation, or by appealing to the accompanying figure, find b gla and c gla

Question: A triple of positive integers a, b, and c is called a Pythagorean triple if a 2 + b 2 = c 2 . Let

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 b = || gla and c= gla

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

a. Show that a² + b² = c².

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

b = || gla and c= gla

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