On a Frobenius problem for polynomials

Abstract

We extend the famous diophantine Frobenius problem to the case of polynomials over a field $k$. Similar to the classical problem, we show that the $n=2$ case of the Frobenius problem for polynomials is easy to solve. In addition, we translate a few results from the Frobenius problem over $\mathbb{Z}$ to $k[t]$ and give an algorithm to solve the Frobenius problem for polynomials over a field $k$ of sufficiently large size.