Let two in the first equation be x 1, x2, and two in the second equation be x 1+ 1, x2+ 1.

From Vieta theorem: x1+x2 =-c.

x 1*x2=a

x 1+ 1+x2+ 1=-a

(x 1+ 1)(x2+ 1)= b

It is concluded that b=- 1 and c = 2+a.

Because x 1 and x2 are integers, △ 1 = c 2-4a = a 2+4 = k 2 (k is an integer).

So: (k-a)(k+a)=4.

So a=0.

So a+b+c= 1.