66 lines
1.3 KiB
Markdown
66 lines
1.3 KiB
Markdown
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---
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id: 5900f4201000cf542c50ff33
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challengeType: 5
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title: 'Problem 180: Rational zeros of a function of three variables'
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forumTopicId: 301816
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---
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## Description
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<section id='description'>
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For any integer n, consider the three functions
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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)
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and their combination
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fn(x,y,z) = f1,n(x,y,z) + f2,n(x,y,z) − f3,n(x,y,z)
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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
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0 < a < b ≤ k and there is (at least) one integer n, so that fn(x,y,z) = 0.
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Let s(x,y,z) = x + y + z.
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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.
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Find u + v.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler180()</code> should return 285196020571078980.
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testString: assert.strictEqual(euler180(), 285196020571078980);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler180() {
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return true;
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}
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euler180();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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