Equation in natural numbers

1. Sep 24, 2008

disregardthat

Hi, I was wondering if anyone could find a solution to this:

$$d^2-ab=e^2-bc=f^2-ac$$

in the natural numbers where not all variables are equal. I don't know how to make a computer program, but if it takes little time, I would really appreciate if I could have a solution to it.

2. Sep 24, 2008

mathman

Let a, b, and c be any square numbers, and let d, e, and f be defined so that the differences are zero. The rest is trivially obvious.

If you want non-zero differences it will be more complicated.

3. Sep 24, 2008

disregardthat

Of course =) thanks (cant believe i didn't think of that)

Any solution a,b,c,d,e,f gives a tetrahedron of side lengths a,b,c,d,e,f where a sphere may be located within touching all sides - if my calculations are correct.