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id	challengeType	title	forumTopicId
5900f4601000cf542c50ff73	5	Problem 243: Resilience	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

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

Challenge Seed

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

euler243();

Solution

// solution required

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