---
id: 5900f54b1000cf542c51005d
challengeType: 5
title: 'Problem 479: Roots on the Rise'
---
## Description
Let ak, bk, and ck represent the three solutions (real or complex numbers) to the expression 1/x = (k/x)2(k+x2) - kx.
For instance, for k = 5, we see that {a5, b5, c5} is approximately {5.727244, -0.363622+2.057397i, -0.363622-2.057397i}.
Let S(n) = Σ (ak+bk)p(bk+ck)p(ck+ak)p for all integers p, k such that 1 ≤ p, k ≤ n.
Interestingly, S(n) is always an integer. For example, S(4) = 51160.
Find S(106) modulo 1 000 000 007.
## Instructions
## Tests
```yml
tests:
- text: euler479() should return 191541795.
testString: 'assert.strictEqual(euler479(), 191541795, "euler479() should return 191541795.");'
```
## Challenge Seed
```js
function euler479() {
// Good luck!
return true;
}
euler479();
```