If S = {a₁, a₂, ?, a_n} is a set of relatively prime positive integers, it is well known that any sufficiently large integer can be expressed as a nonnegative integral combination of the elements of S. The Frobenius problem consists of determining how large is sufficiently large. That is, find the smallest possible integer L = (a₁, a₂, ?, a_n) with the property that any number greater than or equal to it can be expressed as a nonnegative integral combination of a₁, a₂, ?, a_n. We review two classical approaches to the problem, and offer a third one. We then apply this latter approach to obtain simplified proofs for several known results and to obtain some new results.

Frobenius number.