Given relatively prime positive integers a1 , ..., an , we call an integer t representable if there exist nonnegative integers m1 , ..., mn such that
We translate this problem into a geometric one: consider N(t), the number of nonnegative integer solutions (m1 , ..., mn ) to m1 a1 + ... + mn an = t for any positive integer t. N(t) enumerates the integer points in a polytope. Solving the Frobenius problem now simply means finding the largest zero of N(t). N(t) turns out to be a quasi-polynomial, thereby yielding a straightforward analytic tool to recover and extend some well-known results on this classical problem.