2018-10-10 18:03:03 -04:00
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---
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id: 5900f4c31000cf542c50ffd5
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2020-12-16 00:37:30 -07:00
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title: 问题342:正方形的总数是一个立方体
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2018-10-10 18:03:03 -04:00
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challengeType: 5
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videoUrl: ''
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2021-01-13 03:31:00 +01:00
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dashedName: problem-342-the-totient-of-a-square-is-a-cube
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2018-10-10 18:03:03 -04:00
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---
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2020-12-16 00:37:30 -07:00
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# --description--
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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考虑数字50. 502 = 2500 = 22×54,因此φ(2500)= 2×4×53 = 8×53 = 23×53.1因此2500是正方形而φ(2500)是立方体。
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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找到所有数字的总和n,1 <n <1010,使得φ(n2)是立方体。
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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1φ表示欧拉的函数。
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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# --hints--
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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`euler342()`应该返回5943040885644。
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2018-10-10 18:03:03 -04:00
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```js
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2020-12-16 00:37:30 -07:00
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assert.strictEqual(euler342(), 5943040885644);
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2018-10-10 18:03:03 -04:00
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```
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2021-01-13 03:31:00 +01:00
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# --seed--
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## --seed-contents--
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```js
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function euler342() {
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return true;
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}
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euler342();
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```
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2020-12-16 00:37:30 -07:00
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# --solutions--
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2020-08-13 17:24:35 +02:00
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2021-01-13 03:31:00 +01:00
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```js
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// solution required
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```
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