linear formulas for Pythagorean triples

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Pythagorean triples

In a^2 + b^2 = c^2, a possible parametrization for a Pythagorean triple (a,b,c) is given by
a = u^2 - v^2 > 0,
b = 2uv > 0,
c = u^2 + v^2 > 0.
So that a + b - c = 2v(u - v) > 0, an even number.

perucho

Re: Pythagorean triples

Yes, dear Perucho, it is the most used way to generate Pythagorean numbers (which is derived e.g. in http://planetmath.org/encyclopedia/DerivationOfPythagoreanTriples.html).
Jussi

Re: Pythagorean triples

Of course my dear friend, I just was clarifying why a + b - c is even, as you wrote this in your new entry, pretty original by the way.
perucho