---
id: 5900f4f91000cf542c51000c
title: 'Problem 397: Triangle on parabola'
challengeType: 5
forumTopicId: 302062
dashedName: problem-397-triangle-on-parabola
---

# --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 &lt; b &lt; c ≤ X.

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

# --hints--

`euler397()` should return 141630459461893730.

```js
assert.strictEqual(euler397(), 141630459461893730);
```

# --seed--

## --seed-contents--

```js
function euler397() {

  return true;
}

euler397();
```

# --solutions--

```js
// solution required
```
