---
id: 5900f4f91000cf542c51000c
challengeType: 5
title: 'Problem 397: Triangle on parabola'
---

## Description
<section id='description'>
On the parabola y = x2/k, three points A(a, a2/k), B(b, b2/k) and C(c, c2/k) are chosen.


Let F(K, X) be the number of the integer quadruplets (k, a, b, c) such that at least one angle of the triangle ABC is 45-degree, with 1 ≤ k ≤ K and -X ≤ a < b < c ≤ X.


For example, F(1, 10) = 41 and F(10, 100) = 12492.
Find F(106, 109).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler397()</code> should return 141630459461893730.
    testString: assert.strictEqual(euler397(), 141630459461893730, '<code>euler397()</code> should return 141630459461893730.');

```

</section>

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

<div id='js-seed'>

```js
function euler397() {
  // Good luck!
  return true;
}

euler397();
```

</div>



</section>

## Solution
<section id='solution'>

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