Assignment:
A student thinks of a polynomial p(x) of arbitrary degree, and non-negative integer coefficients. How can you determine the student's polynomial by asking for two values of her polynomial, say p(a) and p(b), where a and b are positive integers? Hint: A positive integer n can be written uniquely in base k, where k is a positive integer. This follows directly by a repeated application of the division algorithm.
Provide complete and step by step solution for the question and show calculations and use formulas.