45 lines
747 B
Markdown
45 lines
747 B
Markdown
---
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id: 5900f4ea1000cf542c50fffc
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title: 'Problem 381: (prime-k) factorial'
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challengeType: 5
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forumTopicId: 302045
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dashedName: problem-381-prime-k-factorial
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---
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# --description--
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For a prime p let S(p) = (∑(p-k)!) mod(p) for 1 ≤ k ≤ 5.
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For example, if p=7, (7-1)! + (7-2)! + (7-3)! + (7-4)! + (7-5)! = 6! + 5! + 4! + 3! + 2! = 720+120+24+6+2 = 872. As 872 mod(7) = 4, S(7) = 4.
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It can be verified that ∑S(p) = 480 for 5 ≤ p < 100.
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Find ∑S(p) for 5 ≤ p < 108.
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# --hints--
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`euler381()` should return 139602943319822.
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```js
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assert.strictEqual(euler381(), 139602943319822);
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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 euler381() {
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return true;
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}
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euler381();
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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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