47 lines
817 B
Markdown
47 lines
817 B
Markdown
---
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id: 5900f5331000cf542c510045
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title: 'Problem 454: Diophantine reciprocals III'
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challengeType: 5
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forumTopicId: 302127
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dashedName: problem-454-diophantine-reciprocals-iii
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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 a limit $L$ we define $F(L)$ as the number of solutions which satisfy $x < y ≤ L$.
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We can verify that $F(15) = 4$ and $F(1000) = 1069$.
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Find $F({10}^{12})$.
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# --hints--
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`diophantineReciprocalsThree()` should return `5435004633092`.
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```js
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assert.strictEqual(diophantineReciprocalsThree(), 5435004633092);
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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 diophantineReciprocalsThree() {
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return true;
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}
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diophantineReciprocalsThree();
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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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