I am neither a mathematician nor do I have an idea on how to write down my problem in accurate mathematic formulas. Please feel free to edit my question into shape and remove this paragraph. Also I am unsure about that tags that apply to this question - problem-solving fits, but maybe there are others?
Given a set of natural numbers:
[125, 70, 55] and a total of 250 (All of these numbers may vary).
Now I need to find the integral factors to the numbers that add up to the total like this:
125*a + 70*b + 55*c = 375
Is there a mathematical solution to this problem or do I have to find out the brute force way?
For this example there is more than one valid solution:
a = 3, b = 0, c = 0
a = 2, b = 1, c = 1
a = 1, b = 2, c = 2
a = 0, b = 3, c = 3
a = 0, b = 1, c = 5
- maybe others...
My goal is it to find all possible solutions - or at least more than one of them.
I already tried some brute force algorithms, but none of them is fast enough to find a solution to this problem for lager numbers.