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id	title	challengeType	forumTopicId	dashedName
5900f42c1000cf542c50ff3f	Problem 192: Best Approximations	5	301830	problem-192-best-approximations

--description--

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.

--hints--

euler192() should return 57060635927998344.

assert.strictEqual(euler192(), 57060635927998344);

--seed--

--seed-contents--

function euler192() {

  return true;
}

euler192();

--solutions--

// solution required

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