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

## Description
<section id='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)?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

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

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

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

euler269();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>