65 lines
1.4 KiB
Markdown
65 lines
1.4 KiB
Markdown
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---
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id: 5
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localeTitle: 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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---
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## Description
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<section id='description'>
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Para cualquier entero n, considere las tres funciones
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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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y su combinación
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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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Llamamos (x, y, z) un triple dorado de orden k si x, y, y z son todos números racionales de la forma a / b con
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0 <a <b ≤ k y hay (al menos) un entero n, de modo que fn (x, y, z) = 0.
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Sea s (x, y, z) = x + y + z.
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Sea t = u / v la suma de todos los s distintos (x, y, z) para todos los triples dorados (x, y, z) de orden 35. Todos los s (x, y, z) yt deben ser En forma reducida.
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Encuentra 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> debe devolver 285196020571078980.
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testString: 'assert.strictEqual(euler180(), 285196020571078980, "<code>euler180()</code> should return 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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// Good luck!
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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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