---
id: 5900f5001000cf542c510012
challengeType: 5
title: 'Problem 404: Crisscross Ellipses'
---

## Description
<section id='description'>
Ea is an ellipse with an equation of the form x2 + 4y2 = 4a2.
Ea' is the rotated image of Ea by θ degrees counterclockwise around the origin O(0, 0) for 0° < θ < 90°.






b is the distance to the origin of the two intersection points closest to the origin and c is the distance of the two other intersection points.
We call an ordered triplet (a, b, c) a canonical ellipsoidal triplet if a, b and c are positive integers.
For example, (209, 247, 286) is a canonical ellipsoidal triplet.



Let C(N) be the number of distinct canonical ellipsoidal triplets (a, b, c) for a ≤ N.
It can be verified that C(103) = 7, C(104) = 106 and C(106) = 11845.



Find C(1017).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler404()</code> should return 1199215615081353.
    testString: assert.strictEqual(euler404(), 1199215615081353, '<code>euler404()</code> should return 1199215615081353.');

```

</section>

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

<div id='js-seed'>

```js
function euler404() {
  // Good luck!
  return true;
}

euler404();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>