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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 \frac{r}{s} in reduced form, with s ≤ d, such that any rational number which is closer to x than \frac{r}{s} has a denominator larger than d:

|\frac{p}{q} - x| &lt; |\frac{r}{s} - x| ⇒ q > d

For example, the best approximation to \sqrt{13} for the denominator bound 20 is \frac{18}{5} and the best approximation to \sqrt{13} for the denominator bound 30 is \frac{101}{28}.

Find the sum of all denominators of the best approximations to \sqrt{n} for the denominator bound {10}^{12}, where n is not a perfect square and 1 < n ≤ 100000.

--hints--

bestApproximations() should return 57060635927998344.

assert.strictEqual(bestApproximations(), 57060635927998344);

--seed--

--seed-contents--

function bestApproximations() {

  return true;
}

bestApproximations();

--solutions--

// solution required

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