Prove that there exist an infinite number of primitive Pythagorean triples x,y, and z with y even such that y is a perfect cube.
I can write down the definition, but I have no idea how prove this...
Any help is appreciated!
[also under discussion in math links forum]
Thanks, but can you explain how you came up with these answers and how can we prove that the resulting triples will all be "primitive" Pythag. triple and that y is a perfect cube?
I have seen the theorem:
The positive primitive solutions of with y even are , where r and s are arbitrary integers of opposite parity with r>s>0 and (r,s)=1.
Thank you!