2018-09-30 22:01:58 +00:00
|
|
|
---
|
|
|
|
id: 5900f4801000cf542c50ff93
|
|
|
|
title: 'Problem 276: Primitive Triangles'
|
2020-11-27 18:02:05 +00:00
|
|
|
challengeType: 5
|
2019-08-05 16:17:33 +00:00
|
|
|
forumTopicId: 301926
|
2021-01-13 02:31:00 +00:00
|
|
|
dashedName: problem-276-primitive-triangles
|
2018-09-30 22:01:58 +00:00
|
|
|
---
|
|
|
|
|
2020-11-27 18:02:05 +00:00
|
|
|
# --description--
|
|
|
|
|
2021-07-24 07:09:54 +00:00
|
|
|
Consider the triangles with integer sides $a$, $b$ and $c$ with $a ≤ b ≤ c$.
|
2018-09-30 22:01:58 +00:00
|
|
|
|
2021-07-24 07:09:54 +00:00
|
|
|
An integer sided triangle $(a,b,c)$ is called primitive if $gcd(a,b,c) = 1$.
|
2018-09-30 22:01:58 +00:00
|
|
|
|
2021-07-24 07:09:54 +00:00
|
|
|
How many primitive integer sided triangles exist with a perimeter not exceeding $10\\,000\\,000$?
|
2018-09-30 22:01:58 +00:00
|
|
|
|
2020-11-27 18:02:05 +00:00
|
|
|
# --hints--
|
2018-09-30 22:01:58 +00:00
|
|
|
|
2021-07-24 07:09:54 +00:00
|
|
|
`primitiveTriangles()` should return `5777137137739633000`.
|
2018-09-30 22:01:58 +00:00
|
|
|
|
2020-11-27 18:02:05 +00:00
|
|
|
```js
|
2021-07-24 07:09:54 +00:00
|
|
|
assert.strictEqual(primitiveTriangles(), 5777137137739633000);
|
2018-09-30 22:01:58 +00:00
|
|
|
```
|
|
|
|
|
2020-11-27 18:02:05 +00:00
|
|
|
# --seed--
|
2018-09-30 22:01:58 +00:00
|
|
|
|
2020-11-27 18:02:05 +00:00
|
|
|
## --seed-contents--
|
2018-09-30 22:01:58 +00:00
|
|
|
|
|
|
|
```js
|
2021-07-24 07:09:54 +00:00
|
|
|
function primitiveTriangles() {
|
2020-09-15 16:57:40 +00:00
|
|
|
|
2018-09-30 22:01:58 +00:00
|
|
|
return true;
|
|
|
|
}
|
|
|
|
|
2021-07-24 07:09:54 +00:00
|
|
|
primitiveTriangles();
|
2018-09-30 22:01:58 +00:00
|
|
|
```
|
|
|
|
|
2020-11-27 18:02:05 +00:00
|
|
|
# --solutions--
|
2018-09-30 22:01:58 +00:00
|
|
|
|
|
|
|
```js
|
|
|
|
// solution required
|
|
|
|
```
|