45 lines
1.1 KiB
Markdown
45 lines
1.1 KiB
Markdown
---
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id: 5900f4831000cf542c50ff95
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title: 'Problem 278: Linear Combinations of Semiprimes'
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challengeType: 5
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forumTopicId: 301928
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dashedName: problem-278-linear-combinations-of-semiprimes
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---
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# --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. For instance, if a1 = 5 and a2 = 7, there are no q1 ≥ 0 and q2 ≥ 0 such that b could be 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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# --hints--
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`euler278()` should return 1228215747273908500.
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```js
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assert.strictEqual(euler278(), 1228215747273908500);
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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 euler278() {
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return true;
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}
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euler278();
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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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