yaworsw/euler-manager

---
:id: 192
:name: Best Approximations
:url: https://projecteuler.net/problem=192
:content: "Let <var>x</var> be a real number.  \nA _best approximation_ to <var>x</var>
  for the _denominator bound_ <var>d</var> is a rational number <var>r</var>/<var>s</var>
  _in reduced form_, with <var>s</var> ≤ <var>d</var>, such that any rational number
  which is closer to <var>x</var> than <var>r</var>/<var>s</var> has a denominator
  larger than <var>d</var>:\n\n|<var>p</var>/<var>q</var>-<var>x</var>| \\< |<var>r</var>/<var>s</var>-<var>x</var>|
  ⇒ <var>q</var> \\> <var>d</var>\n\nFor example, the best approximation to √13 for
  the denominator bound 20 is 18/5 and the best approximation to √13 for the denominator
  bound 30 is 101/28.\n\nFind the sum of all denominators of the best approximations
  to √<var>n</var> for the denominator bound 10<sup>12</sup>, where <var>n</var> is
  not a perfect square and 1 \\< <var>n</var> ≤ 100000.\n\n"