Apologies for the stupid question title. I've been given a non-graded challenge in Java to essentially determine if there exists two positive integers x and y such that ax+by=c, where a, b, and c are provided.
The context for this is that you're given two coins of value a and b, and you must determine whether they can be combined in some fashion to equal the amount c. The catch to this is your code must not include loops of any kind or recursive functions.
So far I've determined Euclid's Algorithm seems useful to this kind of problem; as finding the greatest common divisor of a and b can prove the existence of x and y as integers that completes the equation. The problem there is that x and y could still be negative, as is the case with the set [3,7,11]. With the greatest common divisor between 3 and 7 being 1, they can be combined to make 11 through 3(-1)+7(2).
Since you obviously can't use a negative amount of coins, 11 wouldn't be a "chicken nugget number" (in reference to the Chicken McNugget problem, which I feel is relevant). So what I'm looking for is either a completely different method of attempting this without loops of any kind, or advice on how to actually determine the values of x and y to see if either are negative.
I'm not necessarily looking for code for this, just any advice or guides would help. If you don't have a solution but are interested in thinking about this, recommended reading is Extended Euclidean Algorithm, Bézout's Identity, Diophantine Equations, and the Chicken McNugget Theorem.