Challenge Question:

Suppose I have a polynomial $\displaystyle p(x) $ with positive integral coefficients. You give me an integer $\displaystyle a $ and I give you $\displaystyle p(a) $. You then give me an integer $\displaystyle b $ and I give you $\displaystyle p(b) $. Your objective is to determine $\displaystyle p(x) $.

How would you do so?