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freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-157-solving-the-diophantine-equation.md
Oliver Eyton-Williams ee1e8abd87 feat(curriculum): restore seed + solution to Chinese (#40683)
* feat(tools): add seed/solution restore script

* chore(curriculum): remove empty sections' markers

* chore(curriculum): add seed + solution to Chinese

* chore: remove old formatter

* fix: update getChallenges

parse translated challenges separately, without reference to the source

* chore(curriculum): add dashedName to English

* chore(curriculum): add dashedName to Chinese

* refactor: remove unused challenge property 'name'

* fix: relax dashedName requirement

* fix: stray tag

Remove stray `pre` tag from challenge file.

Signed-off-by: nhcarrigan <nhcarrigan@gmail.com>

Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
2021-01-12 19:31:00 -07:00

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---
id: 5900f4091000cf542c50ff1c
title: 'Problem 157: Solving the diophantine equation'
challengeType: 5
forumTopicId: 301788
dashedName: problem-157-solving-the-diophantine-equation
---
# --description--
Consider the diophantine equation 1/a+1/b= p/10n with a, b, p, n positive integers and a ≤ b.
For n=1 this equation has 20 solutions that are listed below:
1/1+1/1=20/10
1/1+1/2=15/10
1/1+1/5=12/10
1/1+1/10=11/10
1/2+1/2=10/10
1/2+1/5=7/10
1/2+1/10=6/10
1/3+1/6=5/10
1/3+1/15=4/10
1/4+1/4=5/10
1/4+1/20=3/10
1/5+1/5=4/10
1/5+1/10=3/10
1/6+1/30=2/10
1/10+1/10=2/10
1/11+1/110=1/10
1/12+1/60=1/10
1/14+1/35=1/10
1/15+1/30=1/10
1/20+1/20=1/10
How many solutions has this equation for 1 ≤ n ≤ 9?
# --hints--
`euler157()` should return 53490.
```js
assert.strictEqual(euler157(), 53490);
```
# --seed--
## --seed-contents--
```js
function euler157() {
return true;
}
euler157();
```
# --solutions--
```js
// solution required
```