1.1 KiB
1.1 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f5231000cf542c510034 | Problem 438: Integer part of polynomial equation's solutions | 5 | 302109 | 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.
assert.strictEqual(euler438(), 2046409616809);
--seed--
--seed-contents--
function euler438() {
return true;
}
euler438();
--solutions--
// solution required