---
id: 5900f42c1000cf542c50ff3f
challengeType: 5
title: 'Problem 192: Best Approximations'
forumTopicId: 301830
---

## Description
<section id='description'>
Let x be a real number.
A best approximation to x for the denominator bound d is a rational number r/s in reduced form, with s ≤ d, such that any rational number which is closer to x than r/s has a denominator larger than d:

|p/q-x| < |r/s-x| ⇒ q > d

For example, the best approximation to √13 for the denominator bound 20 is 18/5 and the best approximation to √13 for the denominator bound 30 is 101/28.

Find the sum of all denominators of the best approximations to √n for the denominator bound 1012, where n is not a perfect square and 1 < n ≤ 100000.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler192()</code> should return 57060635927998344.
    testString: assert.strictEqual(euler192(), 57060635927998344);

```

</section>

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

<div id='js-seed'>

```js
function euler192() {

  return true;
}

euler192();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>