freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-269-polynomials-with-at-least-one-integer-root.english.md

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

Description

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)?

Instructions

Tests

tests:
  - text: <code>euler269()</code> should return 1311109198529286.
    testString: assert.strictEqual(euler269(), 1311109198529286);

Challenge Seed

function euler269() {
  // Good luck!
  return true;
}

euler269();

Solution

// solution required