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.

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step-by-step explanation:

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.