47 lines
1.0 KiB
Markdown
47 lines
1.0 KiB
Markdown
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---
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id: 5900f42c1000cf542c50ff3f
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title: 'Problem 192: Best Approximations'
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challengeType: 5
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forumTopicId: 301830
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dashedName: problem-192-best-approximations
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---
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# --description--
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Let x be a real number.
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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:
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|p/q-x| < |r/s-x| ⇒ q > d
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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.
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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.
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# --hints--
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`euler192()` should return 57060635927998344.
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```js
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assert.strictEqual(euler192(), 57060635927998344);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler192() {
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return true;
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}
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euler192();
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```
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# --solutions--
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```js
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// solution required
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```
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