45 lines
827 B
Markdown
45 lines
827 B
Markdown
|
---
|
|||
|
|
id: 5900f3ef1000cf542c50ff02
|
|||
|
|
title: 'Problem 131: Prime cube partnership'
|
|||
|
|
challengeType: 5
|
|||
|
|
forumTopicId: 301759
|
|||
|
|
dashedName: problem-131-prime-cube-partnership
|
|||
|
|
---
|
|||
|
|
|
|||
|
|
# --description--
|
|||
|
|
|
|||
|
|
There are some prime values, p, for which there exists a positive integer, n, such that the expression n3 + n2p is a perfect cube.
|
|||
|
|
|
|||
|
|
For example, when p = 19, 83 + 82×19 = 123.
|
|||
|
|
|
|||
|
|
What is perhaps most surprising is that for each prime with this property the value of n is unique, and there are only four such primes below one-hundred.
|
|||
|
|
|
|||
|
|
How many primes below one million have this remarkable property?
|
|||
|
|
|
|||
|
|
# --hints--
|
|||
|
|
|
|||
|
|
`euler131()` should return 173.
|
|||
|
|
|
|||
|
|
```js
|
|||
|
|
assert.strictEqual(euler131(), 173);
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
# --seed--
|
|||
|
|
|
|||
|
|
## --seed-contents--
|
|||
|
|
|
|||
|
|
```js
|
|||
|
|
function euler131() {
|
|||
|
|
|
|||
|
|
return true;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
euler131();
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
# --solutions--
|
|||
|
|
|
|||
|
|
```js
|
|||
|
|
// solution required
|
|||
|
|
```
|