And went for LOTS of easy with this example as could make something that looks harder but is extra work for nothing. That would be an illusion as is so easy to do.

Like:

**(x**

^{2}+ 2y^{2})(u^{2}+ 3v^{2})(x'^{2}+ 4y'^{2})(u'^{2}+ 5v'^{2}) = p^{2}+ 359q^{2}And finding integer solutions for all the variables is easy. Coming up with variables is harder. But yeah you can just keep going as far as you want.

x = 1, y = 2, u = 2, v = 2, x' = 3, y' = 2, u' = 4, v' = 2, p = 358, q = 2

Using first iteration and using positive as all will get squared. So:

(1 + 8)(4 + 12)(9 + 16)(16 + 20) = (358

^{2}+ 359*4)

Which is:

(9)(16)(25)(36) = (358

^{2}+ 359*4) = 129600

Which worked. Used easy first iterations. Of course iterators work out to infinity.

Just playing around.

James Harris