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* fix: clean-up Project Euler 121-140 * fix: corrections from review Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: missing backticks Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: missing delimiter Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
57 lines
1.0 KiB
Markdown
57 lines
1.0 KiB
Markdown
---
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id: 5900f3ec1000cf542c50fefe
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title: 'Problem 127: abc-hits'
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challengeType: 5
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forumTopicId: 301754
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dashedName: problem-127-abc-hits
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---
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# --description--
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The radical of $n$, $rad(n)$, is the product of distinct prime factors of $n$. For example, $504 = 2^3 × 3^2 × 7$, 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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1. $GCD(a, b) = GCD(a, c) = GCD(b, c) = 1$
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2. $a < b$
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3. $a + b = c$
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4. $rad(abc) < c$
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For example, (5, 27, 32) is an abc-hit, because:
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1. $GCD(5, 27) = GCD(5, 32) = GCD(27, 32) = 1$
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2. $5 < 27$
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3. $5 + 27 = 32$
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4. $rad(4320) = 30 < 32$
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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 $\sum{c} = 12523$.
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Find $\sum{c}$ for $c < 120000$.
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# --hints--
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`abcHits()` should return `18407904`.
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```js
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assert.strictEqual(abcHits(), 18407904);
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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 abcHits() {
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return true;
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}
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abcHits();
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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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