d269909faa
* fix: clean-up Project Euler 381-400 * fix: missing image extension * fix: missing subscripts Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
49 lines
837 B
Markdown
49 lines
837 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 $S(p) = (\sum (p - k)!)\bmod (p)$ for $1 ≤ k ≤ 5$.
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For example, if $p = 7$,
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$$(7 - 1)! + (7 - 2)! + (7 - 3)! + (7 - 4)! + (7 - 5)! = 6! + 5! + 4! + 3! + 2! = 720 + 120 + 24 + 6 + 2 = 872$$
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As $872\bmod (7) = 4$, $S(7) = 4$.
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It can be verified that $\sum S(p) = 480$ for $5 ≤ p < 100$.
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Find $\sum S(p)$ for $5 ≤ p < {10}^8$.
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# --hints--
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`primeKFactorial()` should return `139602943319822`.
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```js
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assert.strictEqual(primeKFactorial(), 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 primeKFactorial() {
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return true;
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}
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primeKFactorial();
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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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