49 lines
976 B
Markdown
49 lines
976 B
Markdown
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---
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id: 5900f48d1000cf542c50ff9f
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title: 'Problem 288: An enormous factorial'
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challengeType: 5
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forumTopicId: 301939
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dashedName: problem-288-an-enormous-factorial
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---
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# --description--
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For any prime $p$ the number $N(p,q)$ is defined by $N(p,q) = \sum_{n=0}^q T_n \times p^n$ with $T_n$ generated by the following random number generator:
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$$\begin{align} & S_0 = 290797 \\\\ & S_{n + 1} = {S_n}^2\bmod 50\\,515\\,093 \\\\ & T_n = S_n\bmod p \end{align}$$
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Let $Nfac(p,q)$ be the factorial of $N(p,q)$.
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Let $NF(p,q)$ be the number of factors $p$ in $Nfac(p,q)$.
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You are given that $NF(3,10000) \bmod 3^{20} = 624\\,955\\,285$.
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Find $NF(61,{10}^7)\bmod {61}^{10}$.
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# --hints--
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`enormousFactorial()` should return `605857431263982000`.
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```js
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assert.strictEqual(enormousFactorial(), 605857431263982000);
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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 enormousFactorial() {
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return true;
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}
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enormousFactorial();
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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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