Ricardo Conceição, Rodrigo Gondim, Miguel Rodriguez
Published 2014-09-15Version 1
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.
Comments: 22 pages, submitted
Newton polygons of $L$-functions of polynomials $x^d+ax^{d-1}$ with $p\equiv-1\bmod d$
Spectra of certain types of polynomials and tiling of integers with translates of finite sets
Polynomials with divisors of every degree
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