# Maximum Flow in a Network

Let $$N = (V, E)$$ be a network in which the capacity of each edge is either $$12$$ or $$18$$.

Prove or disprove: The value of a maximum flow for $$N$$ can’t be $$56$$.

I'm trying to figure out how to definitely prove this. I think that this is not possible because of no combination of $$12X + 18Y$$ (where $$X$$ and $$Y$$ are integers) will ever $$= 56$$. Is there a better way of saying this? Am I right to say that an integer solution to $$12X + 18Y = 56$$ is what the Fold-Fulkerson algorithm implies?