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---
id: 5900f4601000cf542c50ff73
title: 'Problem 243: Resilience'
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challengeType: 5
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forumTopicId: 301890
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dashedName: problem-243-resilience
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---
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# --description--
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A positive fraction whose numerator is less than its denominator is called a proper fraction.
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For any denominator, $d$, there will be $d− 1$ proper fractions; for example, with $d = 12$:
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$$\frac{1}{12}, \frac{2}{12}, \frac{3}{12}, \frac{4}{12}, \frac{5}{12}, \frac{6}{12}, \frac{7}{12}, \frac{8}{12}, \frac{9}{12}, \frac{10}{12}, \frac{11}{12}$$
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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, $R(12) = \frac{4}{11}$.
In fact, $d = 12$ is the smallest denominator having a resilience $R(d) < \frac{4}{10}$.
Find the smallest denominator $d$, having a resilience $R(d) < \frac{15\\,499}{94\\,744}$.
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# --hints--
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`resilience()` should return `892371480` .
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```js
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assert.strictEqual(resilience(), 892371480);
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```
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# --seed--
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## --seed-contents--
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```js
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function resilience() {
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return true;
}
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resilience();
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```
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# --solutions--
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```js
// solution required
```