freeCodeCamp/curriculum/challenges/chinese/10-coding-interview-prep/project-euler/problem-157-solving-the-diophantine-equation.md

---
id: 5900f4091000cf542c50ff1c
challengeType: 5
videoUrl: ''
title: 问题157：解决丢番图方程
---

## Description
<section id="description">
491/5000
考虑具有a，b，p，n个正整数且a≤b的双色子方程1 / a + 1 / b = p / 10n。
对于n = 1，此等式有20个解决方案，如下所示：
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
1/14 + 1/35 = 1/10
1/15 + 1/30 = 1/10
1/20 + 1/20 = 1/10
对于1≤n≤9，该方程有多少个解？
</section>

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

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler157()</code>应返回53490。
    testString: assert.strictEqual(euler157(), 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>