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id	title	challengeType	forumTopicId	dashedName
5900f4601000cf542c50ff73	Problem 243: Resilience	5	301890	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:

\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}

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}.

--hints--

resilience() should return 892371480.

assert.strictEqual(resilience(), 892371480);

--seed--

--seed-contents--

function resilience() {

  return true;
}

resilience();

--solutions--

// solution required

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