45 lines
1.1 KiB
Markdown
45 lines
1.1 KiB
Markdown
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---
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id: 5900f5231000cf542c510034
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title: 'Problem 438: Integer part of polynomial equation''s solutions'
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challengeType: 5
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forumTopicId: 302109
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dashedName: problem-438-integer-part-of-polynomial-equations-solutions
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---
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# --description--
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For an n-tuple of integers t = (a1, ..., an), let (x1, ..., xn) be the solutions of the polynomial equation xn + a1xn-1 + a2xn-2 + ... + an-1x + an = 0.
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Consider the following two conditions: x1, ..., xn are all real. If x1, ..., xn are sorted, ⌊xi⌋ = i for 1 ≤ i ≤ n. (⌊·⌋: floor function.)
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In the case of n = 4, there are 12 n-tuples of integers which satisfy both conditions. We define S(t) as the sum of the absolute values of the integers in t. For n = 4 we can verify that ∑S(t) = 2087 for all n-tuples t which satisfy both conditions.
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Find ∑S(t) for n = 7.
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# --hints--
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`euler438()` should return 2046409616809.
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```js
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assert.strictEqual(euler438(), 2046409616809);
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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 euler438() {
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return true;
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}
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euler438();
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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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