freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-438-integer-part-of-polynomial-equations-solutions.md

---
id: 5900f5231000cf542c510034
challengeType: 5
title: 'Problem 438: Integer part of polynomial equation''s solutions'
forumTopicId: 302109
---

## Description
<section id='description'>
For an n-tuple of integers t = (a1, ..., an), let (x1, ..., xn) be the solutions of the polynomial equation xn + a1xn-1 + a2xn-2 + ... + an-1x + an = 0.


Consider the following two conditions:
x1, ..., xn are all real.
If x1, ..., xn are sorted, ⌊xi⌋ = i for 1 ≤ i ≤ n. (⌊·⌋: floor function.)

In the case of n = 4, there are 12 n-tuples of integers which satisfy both conditions.
We define S(t) as the sum of the absolute values of the integers in t.
For n = 4 we can verify that ∑S(t) = 2087 for all n-tuples t which satisfy both conditions.


Find ∑S(t) for n = 7.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler438()</code> should return 2046409616809.
    testString: assert.strictEqual(euler438(), 2046409616809);

```

</section>

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

<div id='js-seed'>

```js
function euler438() {

  return true;
}

euler438();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>