---
id: 5900f4601000cf542c50ff73
challengeType: 5
title: 'Problem 243: Resilience'
---

## Description
<section id='description'>
A positive fraction whose numerator is less than its denominator is called a proper fraction.
For any denominator, d, there will be d−1 proper fractions; for example, with d = 12:1/12 , 2/12 , 3/12 , 4/12 , 5/12 , 6/12 , 7/12 , 8/12 , 9/12 , 10/12 , 11/12 .


We shall call a fraction that cannot be cancelled down a resilient fraction.
Furthermore we shall define the resilience of a denominator, R(d), to be the ratio of its proper fractions that are resilient; for example, R(12) = 4/11 .
In fact, d = 12 is the smallest denominator having a resilience R(d) < 4/10 .

Find the smallest denominator d, having a resilience R(d) < 15499/94744 .
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler243()</code> should return 892371480.
    testString: assert.strictEqual(euler243(), 892371480, '<code>euler243()</code> should return 892371480.');

```

</section>

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

<div id='js-seed'>

```js
function euler243() {
  // Good luck!
  return true;
}

euler243();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>