Numbers a, b and c form an arithmetic sequence if b − a = c − b. Let a, b, c be positive

integers forming an arithmetic sequence with a < b < c. Let f(x) = ax^2 + bx + c. Two distinct

real numbers r and s satisfy f(r) = s and f(s) = r. If rs = 2017, determine the smallest possible

value of a.

I tried changing b and c into a+d and a+2d to get (r-s)((r+s+1)a+(d+1))=0 but I am stuck on how to show the least possible value of a.