freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-180-rational-zeros-...

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---
id: 5900f4201000cf542c50ff33
title: 'Problem 180: Rational zeros of a function of three variables'
challengeType: 5
forumTopicId: 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.
# --hints--
`euler180()` should return 285196020571078980.
```js
assert.strictEqual(euler180(), 285196020571078980);
```
# --seed--
## --seed-contents--
```js
function euler180() {
return true;
}
euler180();
```
# --solutions--
```js
// solution required
```