freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-269-polynomials-with-at-least-one-integer-root.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f4791000cf542c50ff8c	Problem 269: Polynomials with at least one integer root	5	301918	problem-269-polynomials-with-at-least-one-integer-root

--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