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---
id: 5900f3ef1000cf542c50ff02
title: '問題 131立方夥伴素數'
challengeType: 5
forumTopicId: 301759
dashedName: problem-131-prime-cube-partnership
---
# --description--
存在一些素數 $p$,使得存在正整數 $n$,讓算式 $n^3 + n^{2}p$ 得到一個立方數。
例如當 $p = 19,\\ 8^3 + 8^2 × 19 = {12}^3$。
最奇特的是 $n$ 的值對於這個素數具有唯一性100 以內只有四個這種素數。
一百萬以下的素數有多少具有這種非凡特性?
# --hints--
`primeCubePartnership()` 應該返回 `173`
```js
assert.strictEqual(primeCubePartnership(), 173);
```
# --seed--
## --seed-contents--
```js
function primeCubePartnership() {
return true;
}
primeCubePartnership();
```
# --solutions--
```js
// solution required
```