f1c9b08cf3
This includes certificates (where it does nothing), but does not include any translations.
69 lines
1.3 KiB
Markdown
69 lines
1.3 KiB
Markdown
---
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id: 5900f4831000cf542c50ff95
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challengeType: 5
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isHidden: false
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title: 'Problem 278: Linear Combinations of Semiprimes'
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forumTopicId: 301928
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---
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## Description
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<section id='description'>
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Given the values of integers 1 < a1 < a2 <... < an, consider the linear combination q1a1 + q2a2 + ... + qnan = b, using only integer values qk ≥ 0.
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Note that for a given set of ak, it may be that not all values of b are possible.
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For instance, if a1 = 5 and a2 = 7, there are no q1 ≥ 0 and q2 ≥ 0 such that b could be
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1, 2, 3, 4, 6, 8, 9, 11, 13, 16, 18 or 23.
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In fact, 23 is the largest impossible value of b for a1 = 5 and a2 = 7. We therefore call f(5, 7) = 23. Similarly, it can be shown that f(6, 10, 15)=29 and f(14, 22, 77) = 195.
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Find ∑ f(p*q,p*r,q*r), where p, q and r are prime numbers and p < q < r < 5000.
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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>euler278()</code> should return 1228215747273908500.
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testString: assert.strictEqual(euler278(), 1228215747273908500);
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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 euler278() {
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// Good luck!
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return true;
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}
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euler278();
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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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