78 lines
1.2 KiB
Markdown
78 lines
1.2 KiB
Markdown
---
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id: 5900f4091000cf542c50ff1c
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challengeType: 5
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title: 'Problem 157: Solving the diophantine equation'
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---
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## Description
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<section id='description'>
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Consider the diophantine equation 1/a+1/b= p/10n 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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1/1+1/1=20/10
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1/1+1/2=15/10
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1/1+1/5=12/10
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1/1+1/10=11/10
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1/2+1/2=10/10
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1/2+1/5=7/10
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1/2+1/10=6/10
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1/3+1/6=5/10
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1/3+1/15=4/10
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1/4+1/4=5/10
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1/4+1/20=3/10
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1/5+1/5=4/10
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1/5+1/10=3/10
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1/6+1/30=2/10
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1/10+1/10=2/10
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1/11+1/110=1/10
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1/12+1/60=1/10
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1/14+1/35=1/10
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1/15+1/30=1/10
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1/20+1/20=1/10
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How many solutions has this equation for 1 ≤ n ≤ 9?
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler157()</code> should return 53490.
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testString: 'assert.strictEqual(euler157(), 53490, ''<code>euler157()</code> should return 53490.'');'
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler157() {
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// Good luck!
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return true;
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}
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euler157();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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