---
id: 5900f5231000cf542c510034
challengeType: 5
title: 'Problem 438: Integer part of polynomial equation''s solutions'
---
## 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.
## Instructions
## Tests
```yml
tests:
- text: euler438() should return 2046409616809.
testString: assert.strictEqual(euler438(), 2046409616809, 'euler438() should return 2046409616809.');
```
## Challenge Seed
```js
function euler438() {
// Good luck!
return true;
}
euler438();
```