fix: replace .english.md extension with .md

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Oliver Eyton-Williams
2020-09-29 19:05:53 +02:00
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---
id: 5900f3ec1000cf542c50fefe
challengeType: 5
title: 'Problem 127: abc-hits'
forumTopicId: 301754
---
## Description
<section id='description'>
The radical of n, rad(n), is the product of distinct prime factors of n. For example, 504 = 23 × 32 × 7, so rad(504) = 2 × 3 × 7 = 42.
We shall define the triplet of positive integers (a, b, c) to be an abc-hit if:
GCD(a, b) = GCD(a, c) = GCD(b, c) = 1
a < b
a + b = c
rad(abc) < c
For example, (5, 27, 32) is an abc-hit, because:
GCD(5, 27) = GCD(5, 32) = GCD(27, 32) = 1
5 < 27
5 + 27 = 32
rad(4320) = 30 < 32
It turns out that abc-hits are quite rare and there are only thirty-one abc-hits for c < 1000, with c = 12523.
Find c for c < 120000.
</section>
## Instructions
<section id='instructions'>
</section>
## Tests
<section id='tests'>
```yml
tests:
- text: <code>euler127()</code> should return 18407904.
testString: assert.strictEqual(euler127(), 18407904);
```
</section>
## Challenge Seed
<section id='challengeSeed'>
<div id='js-seed'>
```js
function euler127() {
return true;
}
euler127();
```
</div>
</section>
## Solution
<section id='solution'>
```js
// solution required
```
</section>