67 lines
1.0 KiB
Markdown
67 lines
1.0 KiB
Markdown
---
|
|
id: 5900f4f21000cf542c510005
|
|
challengeType: 5
|
|
title: 'Problem 390: Triangles with non rational sides and integral area'
|
|
forumTopicId: 302055
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
Consider the triangle with sides √5, √65 and √68.
|
|
It can be shown that this triangle has area 9.
|
|
|
|
S(n) is the sum of the areas of all triangles with sides √(1+b2), √(1+c2) and √(b2+c2) (for positive integers b and c ) that have an integral area not exceeding n.
|
|
|
|
The example triangle has b=2 and c=8.
|
|
|
|
S(106)=18018206.
|
|
|
|
Find S(1010).
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler390()</code> should return 2919133642971.
|
|
testString: assert.strictEqual(euler390(), 2919133642971);
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler390() {
|
|
|
|
return true;
|
|
}
|
|
|
|
euler390();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
|
|
</section>
|