On a Frobenius problem for polynomials

2014/09/15 by Conceição, Ricardo, Gondim, Rodrigo, Rodriguez, Miguel
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1409.4129

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 ℤ to k[t] and give an algorithm to solve the Frobenius problem for polynomials over a field k of sufficiently large size.

Related

• The Frobenius problem over real number fields
• A geometric approach to the diophantine Frobenius problem
• Counting polynomials over finite fields with given root multiplicities
• Refined upper bounds for the linear Diophantine problem of Frobenius
• The Diophantine Frobenius Problem revisited