43 lines
874 B
Markdown
43 lines
874 B
Markdown
---
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id: 5900f4da1000cf542c50ffec
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title: 'Problem 365: A huge binomial coefficient'
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challengeType: 5
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forumTopicId: 302026
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dashedName: problem-365-a-huge-binomial-coefficient
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---
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# --description--
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The binomial coefficient $\displaystyle\binom{{10}^{18}}{{10}^9}$ is a number with more than 9 billion ($9 × {10}^9$) digits.
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Let $M(n, k, m)$ denote the binomial coefficient $\displaystyle\binom{n}{k}$ modulo $m$.
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Calculate $\sum M({10}^{18}, {10}^9, p \times q \times r)$ for $1000 < p < q < r < 5000$ and $p$, $q$, $r$ prime.
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# --hints--
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`hugeBinomialCoefficient()` should return `162619462356610300`.
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```js
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assert.strictEqual(hugeBinomialCoefficient(), 162619462356610300);
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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 hugeBinomialCoefficient() {
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return true;
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}
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hugeBinomialCoefficient();
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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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