2018-10-10 22:03:03 +00:00
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---
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id: 5900f48d1000cf542c50ff9f
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2020-12-16 07:37:30 +00:00
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title: 问题288:一个巨大的阶乘
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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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---
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2020-12-16 07:37:30 +00:00
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# --description--
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2020-02-17 16:40:55 +00:00
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2020-12-16 07:37:30 +00:00
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对于任何素数p,数N(p,q)定义为
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2020-02-17 16:40:55 +00:00
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2020-12-16 07:37:30 +00:00
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N(p,q)= ∑n = 0至q Tn \* pn,其中Tn由以下随机数生成器生成:
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2020-02-17 16:40:55 +00:00
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2020-12-16 07:37:30 +00:00
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S0 = 290797 Sn + 1 = Sn2 mod 50515093 Tn = Sn mod p
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2020-02-17 16:40:55 +00:00
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2020-12-16 07:37:30 +00:00
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令Nfac(p,q)为N(p,q)的阶乘。 令NF(p,q)为Nfac(p,q)中因子p的数量。
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2020-02-17 16:40:55 +00:00
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给出NF(3,10000)mod 320 = 624955285。
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求NF(61,107)mod 6110
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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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`euler288()`应该返回605857431263982000。
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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(euler288(), 605857431263982000);
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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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# --solutions--
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2020-08-13 15:24:35 +00:00
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