Pythagorean anti-Triples?
Ask your class if there are any Pythagorean anti-Triples: \(\dfrac{1}{a^2} + \dfrac{1}{b^2} = \dfrac{1}{c^2}\) ?
If a, b, c are integers, the question seems harder, since 1/3, 1/4, 1/5 would be (to me) obvious answers - leading to the rules for Pythagorean triples and just using their reciprocals.
Are there any Pythagorean anti-triples: 1/(a^2) + 1/(b^2) = 1/(c^2) ?
- James Tanton (@jamestanton) October 11, 2015
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