---
id: 5900f4601000cf542c50ff73
challengeType: 5
title: 'Problem 243: Resilience'
forumTopicId: 301890
---
## 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 .
## Instructions
## Tests
```yml
tests:
- text: euler243() should return 892371480.
testString: assert.strictEqual(euler243(), 892371480);
```
## Challenge Seed
```js
function euler243() {
// Good luck!
return true;
}
euler243();
```