Prove diophantine equation $S^2+R^2+(r_1-r_2)^2 = 2R(r_1+r_2)$ has at most one solution Given this diophantine equation:
$$S^2+R^2+(r_1-r_2)^2 = 2R(r_1+r_2)$$
$S,r_1,r_2$ are variables. $R$ is a given constant. all values are positive integers.
How do I prove that there's at most one solution, not counting solutions where $r_1$ and $r_2$ are exchanged.
Thanks.

For the equation.
$$S^2+R^2+(x-y)^2=2R(x+y)$$
You can set some numbers infinitely different way.
$$R=(a-b)^2+(c-d)^2$$
Then decisions can be recorded.
$$S=2(cb-ad)$$
$$x=b^2+d^2$$
$$y=a^2+c^2$$
