ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
45 lines
1.1 KiB
Markdown
45 lines
1.1 KiB
Markdown
---
|
|
id: 5900f4831000cf542c50ff95
|
|
title: 'Problem 278: Linear Combinations of Semiprimes'
|
|
challengeType: 5
|
|
forumTopicId: 301928
|
|
dashedName: problem-278-linear-combinations-of-semiprimes
|
|
---
|
|
|
|
# --description--
|
|
|
|
Given the values of integers 1 < a1 < a2 <... < an, consider the linear combination q1a1 + q2a2 + ... + qnan = b, using only integer values qk ≥ 0.
|
|
|
|
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.
|
|
|
|
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.
|
|
|
|
Find ∑ f(p*q,p*r,q\*r), where p, q and r are prime numbers and p < q < r < 5000.
|
|
|
|
# --hints--
|
|
|
|
`euler278()` should return 1228215747273908500.
|
|
|
|
```js
|
|
assert.strictEqual(euler278(), 1228215747273908500);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function euler278() {
|
|
|
|
return true;
|
|
}
|
|
|
|
euler278();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|