Suppose that m and n are positive integers with m > n. If a = m^2 - n^2, b = 2mn, and c = m^2 + n^2, show that a, b, and c are the lengths of the sides of a right triangle. Note: Provide the steps leading to the prove.
Assuming c is intended to be the hypotenuse, these lengths will form a right triangle if, and only if, a^2 + b^2 = c^2 (the Pythagorean Theorem). So replace a, b, and c by their expressions, and show that both sides are equal by expanding (distributing).
If this doesn't work (in fact, it will), you would try again taking a different side as the hypotenuse.
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