---
id: 5900f4831000cf542c50ff95
challengeType: 5
title: 'Problem 278: Linear Combinations of Semiprimes'
---
## Description
Given the values of integers 1 < a1 < a2 <... < an, consider the linear combinationq1a1 + 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.
## Instructions
## Tests
```yml
tests:
- text: euler278() should return 1228215747273908500.
testString: assert.strictEqual(euler278(), 1228215747273908500, 'euler278() should return 1228215747273908500.');
```
## Challenge Seed
```js
function euler278() {
// Good luck!
return true;
}
euler278();
```