Then I think maybe there is some problem with the method you suggested earlier?

The triple x+y,x-y,2z is not necessarily primitive, so I think we should use (i) rather than the theorem in my first post?

<=> x+y,x-y,2z is a Pythagorean triple (but it's not necessarily primitive)

where d is natural number, m and n are integers of opposite parity with m>n>0 and gcd(m,n)=1.

Now how can we characterize ALL solutions of ? Is there any restriction on "d"?

Thanks!