---
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.

$$\frac{1}{x} + \frac{1}{y} = \frac{1}{n}$$

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 $F({10}^{12})$.

# --hints--

`diophantineReciprocalsThree()` should return `5435004633092`.

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

# --seed--

## --seed-contents--

```js
function diophantineReciprocalsThree() {

  return true;
}

diophantineReciprocalsThree();
```

# --solutions--

```js
// solution required
```