Let b and c be integers in the set −6,−5,−4,−3,−2,−1,0,1,2,3,4,5,6 (Note that b and c can be equal.) For how many choices of b and c is it true that the roots of x2+bx+c are consecutive integers?
There are 6 + 7 + 8 = 21 choices for b and c.
