397a9f0c3e
* fix: clean-up Project Euler 462-480 * fix: missing image extension * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
47 lines
1.0 KiB
Markdown
47 lines
1.0 KiB
Markdown
---
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id: 5900f54b1000cf542c51005d
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title: 'Problem 479: Roots on the Rise'
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challengeType: 5
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forumTopicId: 302156
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dashedName: problem-479-roots-on-the-rise
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---
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# --description--
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Let $a_k$, $b_k$, and $c_k$ represent the three solutions (real or complex numbers) to the expression $\frac{1}{x} = {\left(\frac{k}{x} \right)}^2 (k + x^2) - kx$.
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For instance, for $k = 5$, we see that $\\{a_5, b_5, c_5\\}$ is approximately $\\{5.727244, -0.363622 + 2.057397i, -0.363622 - 2.057397i\\}$.
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Let $S(n) = \displaystyle\sum_{p = 1}^n \sum_{k = 1}^n {(a_k + b_k)}^p {(b_k + c_k)}^p {(c_k + a_k)}^p$ for all integers $p$, $k$ such that $1 ≤ p, k ≤ n$.
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Interestingly, $S(n)$ is always an integer. For example, $S(4) = 51\\,160$.
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Find $S({10}^6) \text{ modulo } 1\\,000\\,000\\,007$.
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# --hints--
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`rootsOnTheRise()` should return `191541795`.
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```js
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assert.strictEqual(rootsOnTheRise(), 191541795);
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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 rootsOnTheRise() {
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return true;
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}
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rootsOnTheRise();
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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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