Second Problem Set

The first part of the problem set where we had to prove that for n > N, n postage can be made with 5-cent and 11-cent stamps was pretty straight forward, since we did a similar question during lecture. Proving the second part of that question was a bit more difficult than I initially thought.

I wrote a small java app to figure out what was the smallest n that the postage can be made consecutively after. The magic number we were looking for was 39. Proving that 39=11x +5y has no solution on the natural number line was a little trouble at first. I was trying to come up with an elaborate proof, but later realized a simple simple proof would suffice. I went to the TA office hour and he mentioned that all that the proof requires are some cases to illustrate that 39=11x +5y has no natural number solutions.

I formulated the proof focusing on 11x, because it has fewer cases than 5y.