---
id: 5900f4f91000cf542c51000c
challengeType: 5
title: '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 < b < c ≤ X.
For example, F(1, 10) = 41 and F(10, 100) = 12492.
Find F(106, 109).
## Instructions
## Tests
```yml
tests:
- text: euler397() should return 141630459461893730.
testString: 'assert.strictEqual(euler397(), 141630459461893730, "euler397() should return 141630459461893730.");'
```
## Challenge Seed
```js
function euler397() {
// Good luck!
return true;
}
euler397();
```