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

---
id: 5900f4091000cf542c50ff1c
title: 问题157：解决丢番图方程
challengeType: 5
videoUrl: ''
dashedName: problem-157-solving-the-diophantine-equation
---

# --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？

# --hints--

`euler157()`应返回53490。

```js
assert.strictEqual(euler157(), 53490);
```

# --seed--

## --seed-contents--

```js
function euler157() {

  return true;
}

euler157();
```

# --solutions--

```js
// solution required
```