70 lines
1.2 KiB
Markdown
70 lines
1.2 KiB
Markdown
---
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id: 5900f3ec1000cf542c50fefe
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challengeType: 5
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title: 'Problem 127: abc-hits'
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forumTopicId: 301754
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---
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## Description
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<section id='description'>
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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.
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We shall define the triplet of positive integers (a, b, c) to be an abc-hit if:
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GCD(a, b) = GCD(a, c) = GCD(b, c) = 1
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a < b
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a + b = c
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rad(abc) < c
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For example, (5, 27, 32) is an abc-hit, because:
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GCD(5, 27) = GCD(5, 32) = GCD(27, 32) = 1
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5 < 27
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5 + 27 = 32
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rad(4320) = 30 < 32
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It turns out that abc-hits are quite rare and there are only thirty-one abc-hits for c < 1000, with ∑c = 12523.
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Find ∑c for c < 120000.
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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>euler127()</code> should return 18407904.
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testString: assert.strictEqual(euler127(), 18407904);
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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 euler127() {
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// Good luck!
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return true;
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}
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euler127();
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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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