The Frobenius Coin Problem

The Frobenius Coin Problem is one of the oldest problems in Linear
Diophantine Analysis. For n = 2, James Sylvester found a formula for the Frobenius
number g(a,b) in 1884. I plan to talk about the history of Diophantine Equations
then focus on the Frobenius Coin Problem (for n = 2). Though this is a combinatorial
problem, I will give a geometric proof instead; it is my own (though probably not
original) and shows the audience a different way to achieve the same result. I will
finish on extensions for n = 3 and bounds/specific cases for certain a, b, and c.