For this question, I know how to find the frobenius number, but I'm not sure how to prove it. Here is what I have so far. Can anyone please help me out?
Let S = {3,8}. Find the Frobenius number of S,F(S). Prove that your answer is correct.
frobenius number = g(a,b)
g(3,8) = 3*8-3-8 = 13
There are two parts to proving this is the Frobenius number for the set $S = \{3,8\}$. First, show that you can produce $14, 15, {\dots}$ as a sum of nonnegative integer multiples of the elements of $S$. Since $\min S = 3$, if you can produce $k$, you can produce $k+3$, so you only need to demonstrate production of $14$, $15$, and $16$, then write how to extend that list by $3$s to get all larger targets. Then, show, perhaps using the extended Euclidean algorithm, that all nonnegative integer multiples of the elements of $S$ do not produce $13$.