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.
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.