48 lines
1.7 KiB
Markdown
48 lines
1.7 KiB
Markdown
---
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id: 5900f4091000cf542c50ff1c
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title: 'Problema 157: Risolvere l''equazione diofantina'
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challengeType: 5
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forumTopicId: 301788
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dashedName: problem-157-solving-the-diophantine-equation
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---
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# --description--
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Considera l'equazione diofantina $\frac{1}{a} + \frac{1}{b} = \frac{p}{{10}^n}$ con $a$, $b$, $p$, $n$ interi positivi e $a ≤ b$.
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Per $n = 1$ questa equazione ha 20 soluzioni che sono elencate di seguito:
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$$\begin{array}{lllll} \frac{1}{1} + \frac{1}{1} = \frac{20}{10} & \frac{1}{1} + \frac{1}{2} = \frac{15}{10} & \frac{1}{1} + \frac{1}{5} = \frac{12}{10} & \frac{1}{1} + \frac{1}{10} = \frac{11}{10} & \frac{1}{2} + \frac{1}{2} = \frac{10}{10} \\\\
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\frac{1}{2} + \frac{1}{5} = \frac{7}{10} & \frac{1}{2} + \frac{1}{10} = \frac{6}{10} & \frac{1}{3} + \frac{1}{6} = \frac{5}{10} & \frac{1}{3} + \frac{1}{15} = \frac{4}{10} & \frac{1}{4} + \frac{1}{4} = \frac{5}{10} \\\\
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\frac{1}{4} + \frac{1}{4} = \frac{5}{10} & \frac{1}{5} + \frac{1}{5} = \frac{4}{10} & \frac{1}{5} + \frac{1}{10} = \frac{3}{10} & \frac{1}{6} + \frac{1}{30} = \frac{2}{10} & \frac{1}{10} + \frac{1}{10} = \frac{2}{10} \\\\
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\frac{1}{11} + \frac{1}{110} = \frac{1}{10} & \frac{1}{12} + \frac{1}{60} = \frac{1}{10} & \frac{1}{14} + \frac{1}{35} = \frac{1}{10} & \frac{1}{15} + \frac{1}{30} = \frac{1}{10} & \frac{1}{20} + \frac{1}{20} = \frac{1}{10} \end{array}$$
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Quante soluzioni ha questa equazione per $1 ≤ n ≤ 9$?
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# --hints--
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`diophantineEquation()` dovrebbe restituire `53490`.
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```js
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assert.strictEqual(diophantineEquation(), 53490);
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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 diophantineEquation() {
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return true;
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}
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diophantineEquation();
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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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