47 lines
903 B
Markdown
47 lines
903 B
Markdown
---
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id: 5900f3d91000cf542c50feeb
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title: 'Problem 108: Diophantine Reciprocals I'
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challengeType: 5
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forumTopicId: 301732
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dashedName: problem-108-diophantine-reciprocals-i
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---
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# --description--
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In the following equation x, y, and n are positive integers.
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$$\frac{1}{x} + \frac{1}{y} = \frac{1}{n}$$
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For `n` = 4 there are exactly three distinct solutions:
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$$\begin{align} & \frac{1}{5} + \frac{1}{20} = \frac{1}{4}\\\\ \\\\ & \frac{1}{6} + \frac{1}{12} = \frac{1}{4}\\\\ \\\\ & \frac{1}{8} + \frac{1}{8} = \frac{1}{4} \end{align}$$
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What is the least value of `n` for which the number of distinct solutions exceeds one-thousand?
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# --hints--
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`diophantineOne()` should return `180180`.
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```js
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assert.strictEqual(diophantineOne(), 180180);
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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 diophantineOne() {
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return true;
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}
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diophantineOne();
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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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