45 lines
765 B
Markdown
45 lines
765 B
Markdown
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---
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id: 5900f4ae1000cf542c50ffbf
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title: 'Problem 320: Factorials divisible by a huge integer'
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challengeType: 5
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forumTopicId: 301977
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dashedName: problem-320-factorials-divisible-by-a-huge-integer
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---
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# --description--
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Let $N(i)$ be the smallest integer $n$ such that $n!$ is divisible by $(i!)^{1234567890}$
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Let $S(u) = \sum N(i)$ for $10 ≤ i ≤ u$.
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$S(1000)=614\\,538\\,266\\,565\\,663$.
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Find $S(1\\,000\\,000)\bmod {10}^{18}$.
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# --hints--
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`divisibleByHugeInteger()` should return `278157919195482660`.
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```js
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assert.strictEqual(divisibleByHugeInteger(), 278157919195482660);
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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 divisibleByHugeInteger() {
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return true;
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}
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divisibleByHugeInteger();
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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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