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* fix: clean-up Project Euler 141-160 * fix: corrections from review Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: use different notation for consistency * Update curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-144-investigating-multiple-reflections-of-a-laser-beam.md Co-authored-by: gikf <60067306+gikf@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
58 lines
1.7 KiB
Markdown
58 lines
1.7 KiB
Markdown
---
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id: 5900f4091000cf542c50ff1c
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title: 'Problem 157: Solving the diophantine equation'
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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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Consider the diophantine equation $\frac{1}{a} + \frac{1}{b} = \frac{p}{{10}^n}$ with $a$, $b$, $p$, $n$ positive integers and $a ≤ b$.
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For $n = 1$ this equation has 20 solutions that are listed below:
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$$\begin{array}{lllll}
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\frac{1}{1} + \frac{1}{1} = \frac{20}{10} & \frac{1}{1} + \frac{1}{2} = \frac{15}{10}
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& \frac{1}{1} + \frac{1}{5} = \frac{12}{10} & \frac{1}{1} + \frac{1}{10} = \frac{11}{10}
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& \frac{1}{2} + \frac{1}{2} = \frac{10}{10} \\\\
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\frac{1}{2} + \frac{1}{5} = \frac{7}{10} & \frac{1}{2} + \frac{1}{10} = \frac{6}{10}
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& \frac{1}{3} + \frac{1}{6} = \frac{5}{10} & \frac{1}{3} + \frac{1}{15} = \frac{4}{10}
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& \frac{1}{4} + \frac{1}{4} = \frac{5}{10} \\\\
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\frac{1}{4} + \frac{1}{4} = \frac{5}{10} & \frac{1}{5} + \frac{1}{5} = \frac{4}{10}
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& \frac{1}{5} + \frac{1}{10} = \frac{3}{10} & \frac{1}{6} + \frac{1}{30} = \frac{2}{10}
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& \frac{1}{10} + \frac{1}{10} = \frac{2}{10} \\\\
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\frac{1}{11} + \frac{1}{110} = \frac{1}{10} & \frac{1}{12} + \frac{1}{60} = \frac{1}{10}
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& \frac{1}{14} + \frac{1}{35} = \frac{1}{10} & \frac{1}{15} + \frac{1}{30} = \frac{1}{10}
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& \frac{1}{20} + \frac{1}{20} = \frac{1}{10}
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\end{array}$$
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How many solutions has this equation for $1 ≤ n ≤ 9$?
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# --hints--
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`diophantineEquation()` should return `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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