47 lines
865 B
Markdown
47 lines
865 B
Markdown
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---
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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 ak, bk, and ck represent the three solutions (real or complex numbers) to the expression 1/x = (k/x)2(k+x2) - kx.
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For instance, for k = 5, we see that {a5, b5, c5} is approximately {5.727244, -0.363622+2.057397i, -0.363622-2.057397i}.
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Let S(n) = Σ (ak+bk)p(bk+ck)p(ck+ak)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) = 51160.
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Find S(106) modulo 1 000 000 007.
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# --hints--
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`euler479()` should return 191541795.
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```js
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assert.strictEqual(euler479(), 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 euler479() {
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return true;
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}
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euler479();
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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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