Pythagorean Help!

cathwelch

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Joined
May 13, 2009
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5
Question:
Show that there exists infinitely many primitive Pythagorean triples x, y, z whose even member x is a perfect square.

I think I can use the face that n is an arbitrary odd integer and then consider the triple 4n^2, n^4-4, and n^4+4. However, I am stuck on how to put it all together.
 
\(\displaystyle (n^4+4)^2 = (n^4-4)^2 + (4n^2)^2\), as required by the Pythagorean Theorem.
 
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