# Problem 192: Best Approximations
Let x be a real number. A best approximation to x for the denominator
bound d is a rational number r/s in reduced form, with s ≤ d, such that
any rational number which is closer to x than r/s has a denominator
larger than d: |p/q-x| < |r/s-x| ⇒ q > d For 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. Find the
sum of all denominators of the best approximations to √n for the
denominator bound 1012, where n is not a perfect square and 1 < n ≤
100000.