yaworsw/euler-manager

---
:id: 243
:name: Resilience
:url: https://projecteuler.net/problem=243
:content: "A positive fraction whose numerator is less than its denominator is called
  a proper fraction.  \nFor any denominator, <var>d</var>, there will be <var>d</var>−1
  proper fractions; for example, with <var>d</var> = 12:  \n<sup>1</sup>/<sub>12</sub>
  , <sup>2</sup>/<sub>12</sub> , <sup>3</sup>/<sub>12</sub> , <sup>4</sup>/<sub>12</sub>
  , <sup>5</sup>/<sub>12</sub> , <sup>6</sup>/<sub>12</sub> , <sup>7</sup>/<sub>12</sub>
  , <sup>8</sup>/<sub>12</sub> , <sup>9</sup>/<sub>12</sub> , <sup>10</sup>/<sub>12</sub>
  , <sup>11</sup>/<sub>12</sub> .\n\nWe shall call a fraction that cannot be cancelled
  down a _resilient fraction_.  \nFurthermore we shall define the _resilience_ of
  a denominator, <var>R</var>(<var>d</var>), to be the ratio of its proper fractions
  that are resilient; for example, <var>R</var>(12) = <sup>4</sup>/<sub>11</sub> .
  \ \nIn fact, <var>d</var> = 12 is the smallest denominator having a resilience <var>R</var>(<var>d</var>)
  \\< <sup>4</sup>/<sub>10</sub> .\n\nFind the smallest denominator <var>d</var>,
  having a resilience <var>R</var>(<var>d</var>) \\< <sup>15499</sup>/<sub>94744</sub>
  .\n\n"