# Problem 269: Polynomials with at least one integer root
A root or zero of a polynomial P(x) is a solution to the equation P(x) =
0. Define Pn as the polynomial whose coefficients are the digits of n.
For example, P5703(x) = 5x3 + 7x2 + 3. We can see that:Pn(0) is the last
digit of n, Pn(1) is the sum of the digits of n, Pn(10) is n
itself.Define Z(k) as the number of positive integers, n, not exceeding
k for which the polynomial Pn has at least one integer root. It can be
verified that Z(100 000) is 14696. What is Z(1016)?