--description--

A root or zero of a polynomial $P(x)$ is a solution to the equation $P(x) = 0$.

Define $P_n$ as the polynomial whose coefficients are the digits of $n$.

For example, $P_{5703}(x) = 5x^3 + 7x^2 + 3$.

We can see that:

• $P_n(0)$ is the last digit of $n$,
• $P_n(1)$ 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 $P_n$ has at least one integer root.

It can be verified that $Z(100\,000)$ is 14696.

What is $Z({10}^{16})$?

--hints--

polynomialsWithOneIntegerRoot() should return 1311109198529286.

assert.strictEqual(polynomialsWithOneIntegerRoot(), 1311109198529286);

--seed--

--seed-contents--

function polynomialsWithOneIntegerRoot() {

  return true;
}

polynomialsWithOneIntegerRoot();

--solutions--

// solution required