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Hello, Poirot!

I know that (x,y,z) = (a^{2}- b^{2}, 2ab, a^{2}+ b^{2}) is a Pythagorean triple.

How to show it is primitive? .i.e. gcd(x,y,z) = 1

I'm not sure how we "show" it, but here is a fact.

For a primitive Pythagorean triple,

. . (One must be even, the other must be odd.)

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The conditions for the triple to be primitive are that gcd(a,b)=1 and a, b are of opposite parity. See Pythagorean triple - Wikipedia, the free encyclopedia.I know that (a^2-b^2,2ab,a^2+b^2) is pythagorean triple. How to show it is primitive? i.e

gcd(x,y,z)=1

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