2018-10-10 22:03:03 +00:00
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---
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id: 5900f4be1000cf542c50ffd0
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2020-12-16 07:37:30 +00:00
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title: 问题337欧拉序列阶梯
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2018-10-10 22:03:03 +00:00
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challengeType: 5
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videoUrl: ''
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2021-01-13 02:31:00 +00:00
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dashedName: problem-337-totient-stairstep-sequences
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2018-10-10 22:03:03 +00:00
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---
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2020-12-16 07:37:30 +00:00
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# --description--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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令{a1,a2,...,an}为长度为n的整数序列,使得:a1 = 6,对于所有1≤i<n:φ(ai)<φ(ai + 1)<ai <ai + 11令S(N)为具有≤N的这种序列的数目。例如,S(10)= 4:{6},{6,8},{6,8,9}和{6,10}。我们可以验证S(100)= 482073668和S(10 000)mod 108 = 73808307。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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找到S(20 000 000)mod 108。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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1φ表示欧拉的函数。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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# --hints--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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`euler337()`应该返回85068035。
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2018-10-10 22:03:03 +00:00
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```js
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2020-12-16 07:37:30 +00:00
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assert.strictEqual(euler337(), 85068035);
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2018-10-10 22:03:03 +00:00
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```
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2021-01-13 02:31:00 +00:00
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# --seed--
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## --seed-contents--
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```js
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function euler337() {
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return true;
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}
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euler337();
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```
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2020-12-16 07:37:30 +00:00
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# --solutions--
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2020-08-13 15:24:35 +00:00
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2021-01-13 02:31:00 +00:00
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```js
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// solution required
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```
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