---
id: 5900f54b1000cf542c51005d
challengeType: 5
title: 'Problem 479: Roots on the Rise'
---

## Description
<section id='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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler479()</code> should return 191541795.
    testString: assert.strictEqual(euler479(), 191541795);

```

</section>

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

<div id='js-seed'>

```js
function euler479() {
  // Good luck!
  return true;
}

euler479();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>