Evaluate for x=1,2,3,4 and set equal to A^2,B^2,C^2,D^2. Then eliminating a,b,c gives A^2 + 3C^2 = D^2 + 3B^2 so what's needed are integers expressible as the sum of a square and 3 times a square in two ways.
Also, (A,C) and (B,D) each have the same parity.
These observations might expedite a computer search or spur more and better analysis.
Posted by xdog
on 2013-08-16 11:54:48