---
id: 5900f4601000cf542c50ff73
title: 'Problem 243: Resilience'
challengeType: 5
forumTopicId: 301890
dashedName: problem-243-resilience
---

# --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 .

# --hints--

`euler243()` should return 892371480.

```js
assert.strictEqual(euler243(), 892371480);
```

# --seed--

## --seed-contents--

```js
function euler243() {

  return true;
}

euler243();
```

# --solutions--

```js
// solution required
```