freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-438-integer-part-of-polynomial-equations-solutions.md

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 = (a_1, \ldots, a_n), let (x_1, \ldots, x_n) be the solutions of the polynomial equation x^n + a_1x^{n - 1} + a_2x^{n - 2} + \ldots + a_{n - 1}x + a_n = 0.

Consider the following two conditions:

• x_1, \ldots, x_n are all real.
• If x_1, ..., x_n are sorted, ⌊x_i⌋ = 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 \sum S(t) = 2087 for all n-tuples t which satisfy both conditions.

Find \sum S(t) for n = 7.

--hints--

polynomialIntegerPart() should return 2046409616809.

assert.strictEqual(polynomialIntegerPart(), 2046409616809);

--seed--

--seed-contents--

function polynomialIntegerPart() {

  return true;
}

polynomialIntegerPart();

--solutions--

// solution required