---
id: 5900f4791000cf542c50ff8c
challengeType: 5
title: '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 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
```yml
tests:
- text: euler269() should return 1311109198529286.
testString: assert.strictEqual(euler269(), 1311109198529286, 'euler269() should return 1311109198529286.');
```
## Challenge Seed
```js
function euler269() {
// Good luck!
return true;
}
euler269();
```