Have arrived at this equation in attempting to factorize a polynomial, and was wondering if there are any solutions in integers (preferably) or rationals (worst case) for it:
$$(r^2 + s^2)(t^2 + v^2) = (r^2t^2 + s^2v^2) + (rv + st)^2$$
Any help much appreciated.
Muchos Gracias mes amigos.
After expanding you find : $2rstv=0$.
Since the equation is symmetrical in all variables, let's try for instance $r=0$.
This leads to : $s^2(t^2+v^2)=s^2v^2+(st)^2$ which are obviously equal. The other substitutions give the same result.
So the solutions are the quadruplets $(r,s,t,v)$ where at least one of the coordinate is zero, making it an infinity of solutions (integer or not).