---
id: 5900f5201000cf542c510032
challengeType: 5
title: 'Problem 435: Polynomials of Fibonacci numbers'
forumTopicId: 302106
---

## Description
<section id='description'>
The Fibonacci numbers {fn, n ≥ 0} are defined recursively as fn = fn-1 + fn-2 with base cases f0 = 0 and f1 = 1.
Define the polynomials {Fn, n ≥ 0} as Fn(x) = ∑fixi for 0 ≤ i ≤ n.
For example, F7(x) = x + x2 + 2x3 + 3x4 + 5x5 + 8x6 + 13x7, and F7(11) = 268357683.
Let n = 1015. Find the sum [∑0≤x≤100 Fn(x)] mod 1307674368000 (= 15!).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler435()</code> should return 252541322550.
    testString: assert.strictEqual(euler435(), 252541322550);

```

</section>

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

<div id='js-seed'>

```js
function euler435() {
  // Good luck!
  return true;
}

euler435();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>