---
id: 5900f4091000cf542c50ff1c
challengeType: 5
title: 'Problem 157: Solving the diophantine equation'
videoUrl: ''
localeTitle: 'Problema 157: Resolviendo la ecuación diofántica'
---

## Description
<section id="description"> Considere la ecuación diofantina 1 / a + 1 / b = p / 10n con a, b, p, n enteros positivos y a ≤ b. Para n = 1, esta ecuación tiene 20 soluciones que se enumeran a continuación: 1/1 + 1/1 = 20/10 1/1 + 1/2 = 15/10 1/1 + 1/5 = 12/10 1/1 + 1/10 = 11/10 1/2 + 1/2 = 10/10 1/2 + 1/5 = 7/10 1/2 + 1/10 = 6/10 1/3 + 1/6 = 5 / 10 1/3 + 1/15 = 4/10 1/4 + 1/4 = 5/10 1/4 + 1/20 = 3/10 1/5 + 1/5 = 4/10 1/5 + 1/10 = 3/10 1/6 + 1/30 = 2/10 1/10 + 1/10 = 2/10 1/11 + 1/110 = 1/10 1/12 + 1/60 = 1/10 10 1/14 + 1/35 = 1/10 1/15 + 1/30 = 1/10 1/20 + 1/20 = 1/10 ¿Cuántas soluciones tiene esta ecuación para 1 ≤ n ≤ 9? </section>

## Instructions
<section id="instructions">
</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler157()</code> debe devolver 53490.
    testString: 'assert.strictEqual(euler157(), 53490, "<code>euler157()</code> should return 53490.");'

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler157() {
  // Good luck!
  return true;
}

euler157();

```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>