70 lines
1.3 KiB
Markdown
70 lines
1.3 KiB
Markdown
---
|
|
id: 5900f4461000cf542c50ff59
|
|
challengeType: 5
|
|
title: 'Problem 218: Perfect right-angled triangles'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
Consider the right angled triangle with sides a=7, b=24 and c=25.
|
|
The area of this triangle is 84, which is divisible by the perfect numbers 6 and 28.
|
|
Moreover it is a primitive right angled triangle as gcd(a,b)=1 and gcd(b,c)=1.
|
|
Also c is a perfect square.
|
|
|
|
We will call a right angled triangle perfect if
|
|
-it is a primitive right angled triangle
|
|
-its hypotenuse is a perfect square
|
|
|
|
We will call a right angled triangle super-perfect if
|
|
-it is a perfect right angled triangle and
|
|
-its area is a multiple of the perfect numbers 6 and 28.
|
|
|
|
|
|
How many perfect right-angled triangles with c≤1016 exist that are not super-perfect?
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler218()</code> should return 0.
|
|
testString: 'assert.strictEqual(euler218(), 0, "<code>euler218()</code> should return 0.");'
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler218() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler218();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
</section>
|