freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-180-rational-zeros-of-a-function-of-three-variables.english.md

id	challengeType	title	forumTopicId
5900f4201000cf542c50ff33	5	Problem 180: Rational zeros of a function of three variables	301816

Description

For any integer n, consider the three functions f1,n(x,y,z) = xn+1 + yn+1 − zn+1f2,n(x,y,z) = (xy + yz + zx)*(xn-1 + yn-1 − zn-1)f3,n(x,y,z) = xyz*(xn-2 + yn-2 − zn-2) and their combination fn(x,y,z) = f1,n(x,y,z) + f2,n(x,y,z) − f3,n(x,y,z) We call (x,y,z) a golden triple of order k if x, y, and z are all rational numbers of the form a / b with 0 < a < b ≤ k and there is (at least) one integer n, so that fn(x,y,z) = 0. Let s(x,y,z) = x + y + z. Let t = u / v be the sum of all distinct s(x,y,z) for all golden triples (x,y,z) of order 35. All the s(x,y,z) and t must be in reduced form. Find u + v.

Instructions

Tests

tests:
  - text: <code>euler180()</code> should return 285196020571078980.
    testString: assert.strictEqual(euler180(), 285196020571078980);

Challenge Seed

function euler180() {
  // Good luck!
  return true;
}

euler180();

Solution

// solution required