2021-05-05 10:13:49 -07:00
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---
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id: 5900f3ef1000cf542c50ff02
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2021-11-17 03:53:39 -08:00
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title: '問題 131:立方夥伴素數'
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2021-05-05 10:13:49 -07:00
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challengeType: 5
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forumTopicId: 301759
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dashedName: problem-131-prime-cube-partnership
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---
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# --description--
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2021-11-17 03:53:39 -08:00
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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。
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2021-11-17 03:53:39 -08:00
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例如當 $p = 19,\\ 8^3 + 8^2 × 19 = {12}^3$。
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2021-11-17 03:53:39 -08:00
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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。
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2021-11-17 03:53:39 -08:00
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一百萬以下的素數有多少具有這種非凡特性?
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2021-05-05 10:13:49 -07:00
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# --hints--
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2021-11-17 03:53:39 -08:00
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`primeCubePartnership()` 應該返回 `173`。
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2021-05-05 10:13:49 -07:00
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```js
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assert.strictEqual(primeCubePartnership(), 173);
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```
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# --seed--
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## --seed-contents--
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```js
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function primeCubePartnership() {
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return true;
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}
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2021-11-17 03:53:39 -08:00
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primeCubePartnership();
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```
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# --solutions--
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```js
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// solution required
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```
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