2018-10-10 22:03:03 +00:00
---
id: 5900f4f91000cf542c51000c
challengeType: 5
title: 'Problem 397: Triangle on parabola'
2019-08-28 13:26:13 +00:00
forumTopicId: 302062
localeTitle: 'Problem 397: Triangle on parabola'
2018-10-10 22:03:03 +00:00
---
## Description
2019-08-28 13:26:13 +00:00
< 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 >
2018-10-10 22:03:03 +00:00
## Instructions
2019-08-28 13:26:13 +00:00
< section id = 'instructions' >
< / section >
2018-10-10 22:03:03 +00:00
## Tests
< section id = 'tests' >
```yml
tests:
2019-08-28 13:26:13 +00:00
- text: < code > euler397()</ code > should return 141630459461893730.
testString: assert.strictEqual(euler397(), 141630459461893730);
2018-10-10 22:03:03 +00:00
```
< / 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
```
2019-08-28 13:26:13 +00:00
2018-10-10 22:03:03 +00:00
< / section >