Math Problem

I choose at random a polynomial (call it a function, f (x)) with only non-negative integer coefficients. You get to choose a number, a, and I will tell you what f (a) is. You then get to choose another number, b, and I will tell you what f (b) is. Devise a method of choosing a and b such that after hearing what f (b) is, you can tell me what the polynomial is (i.e., what the coefficients are). Propose your answer in the Comments. You may not participate if you knew the answer before reading this post. I assure you no post-high school math skills are required to solve this problem.

Question About Beliefs and Rabbinic Leaders

Question: To what extent are the rabbinic leaders of the Torah community (however their identity is determined) empowered by the Torah to rule upon what must be regarded as false? It is presumably within their authority to rule that polytheism must be regarded as falsehood. It is presumably not within their authority to rule that monotheism must be regarded as falsehood. Are they empowered to rule that it is forbidden to believe that the Code of Hammurabi preceded the giving of the Torah on Mt. Sinai? Are they empowered to rule that it is forbidden to believe Julius Caesar lived? Are they empowered to rule that it is forbidden to believe Louis XIV was king of France? Are they empowered to rule that it is forbidden to believe there is such a thing as a molecule? Are they empowered to rule that it is forbidden to believe I have a right foot? Are they empowered to rule that it is forbidden to believe that I exist? Obviously, there is a line somewhere, beyond which they are not empowered to dictate beliefs. I very much doubt that it can be simply defined. What is it? Responses please.