---
id: 5900f5331000cf542c510045
title: 'Problem 454: Diophantine reciprocals III'
challengeType: 5
forumTopicId: 302127
dashedName: problem-454-diophantine-reciprocals-iii
---

# --description--

In the following equation x, y, and n are positive integers. 1/x + 1/y= 1/n

<!-- TODO Use MathJax -->

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

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

# --hints--

`euler454()` should return 5435004633092.

```js
assert.strictEqual(euler454(), 5435004633092);
```

# --seed--

## --seed-contents--

```js
function euler454() {

  return true;
}

euler454();
```

# --solutions--

```js
// solution required
```