Prove: If a is any integer and the polynomial f(x) = x 2 + ax + 1 factors (poly mod 9), then there are THREE distinct non-negative integers y less than 9 such that f(y) ≡ 0 (mod 9). Hint: If x 2 +ax+ 1 ≡ (x+b)·(x+c) (mod 9), what can you deduce about b and c? Remark: This problem is very similar to the next problem.