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>
47 lines
918 B
Markdown
47 lines
918 B
Markdown
---
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id: 5900f4ed1000cf542c50ffff
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title: 'Problem 383: Divisibility comparison between factorials'
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challengeType: 5
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forumTopicId: 302047
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dashedName: problem-383-divisibility-comparison-between-factorials
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---
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# --description--
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Let $f_5(n)$ be the largest integer $x$ for which $5^x$ divides $n$.
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For example, $f_5(625\\,000) = 7$.
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Let $T_5(n)$ be the number of integers $i$ which satisfy $f_5((2 \times i - 1)!) < 2 \times f_5(i!)$ and $1 ≤ i ≤ n$.
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It can be verified that $T_5({10}^3) = 68$ and $T_5({10}^9) = 2\\,408\\,210$.
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Find $T_5({10}^{18})$.
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# --hints--
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`factorialDivisibilityComparison()` should return `22173624649806`.
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```js
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assert.strictEqual(factorialDivisibilityComparison(), 22173624649806);
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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 factorialDivisibilityComparison() {
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return true;
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}
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factorialDivisibilityComparison();
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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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