MathNet 2012 Question 84

If $a$, $b$, $c$, $d$ are integers and $A = 2(a-2b+c)^{4} + 2(b-2c+a)^{4} + 2(c-2a+b)^{4}$, $B = d(d+1)(d+2)(d+3) + 1$, prove that $(\sqrt{A} + 1)^{2} + B$ cannot be a perfect square.