---
id: 5900f4091000cf542c50ff1c
challengeType: 5
title: 'Problem 157: Solving the diophantine equation'
---

## Description
<section id='description'>
Consider the diophantine equation 1/a+1/b= p/10n with a, b, p, n positive integers and a ≤ b.
For n=1 this equation has 20 solutions that are listed below:
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
How many solutions has this equation for 1 ≤ n ≤ 9?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler157()</code> should return 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>
