---
id: 5900f5331000cf542c510045
challengeType: 5
title: 'Problem 454: Diophantine reciprocals III'
---

## Description
<section id='description'>
In the following equation x, y, and n are positive integers.

1x
 +
1y
 =
1n

For a limit L we define F(L) as the number of solutions which satisfy x < y ≤ L.

We can verify that F(15) = 4 and F(1000) = 1069.
Find F(1012).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler454()</code> should return 5435004633092.
    testString: assert.strictEqual(euler454(), 5435004633092, '<code>euler454()</code> should return 5435004633092.');

```

</section>

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

<div id='js-seed'>

```js
function euler454() {
  // Good luck!
  return true;
}

euler454();
```

</div>



</section>

## Solution
<section id='solution'>

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