ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
45 lines
1.1 KiB
Markdown
45 lines
1.1 KiB
Markdown
---
|
|
id: 5900f5231000cf542c510034
|
|
title: 'Problem 438: Integer part of polynomial equation''s solutions'
|
|
challengeType: 5
|
|
forumTopicId: 302109
|
|
dashedName: problem-438-integer-part-of-polynomial-equations-solutions
|
|
---
|
|
|
|
# --description--
|
|
|
|
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.
|
|
|
|
Consider the following two conditions: x1, ..., xn are all real. If x1, ..., xn are sorted, ⌊xi⌋ = i for 1 ≤ i ≤ n. (⌊·⌋: floor function.)
|
|
|
|
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.
|
|
|
|
Find ∑S(t) for n = 7.
|
|
|
|
# --hints--
|
|
|
|
`euler438()` should return 2046409616809.
|
|
|
|
```js
|
|
assert.strictEqual(euler438(), 2046409616809);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function euler438() {
|
|
|
|
return true;
|
|
}
|
|
|
|
euler438();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|