Rocky Mountain Journal of Mathematics

On a Frobenius problem for polynomials

R. Conceição, R. Gondim, and M. Rodriguez

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We extend the famous diophantine Frobenius problem to a ring 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.

Article information

Rocky Mountain J. Math., Volume 47, Number 5 (2017), 1427-1462.

First available in Project Euclid: 22 September 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11D07: The Frobenius problem
Secondary: 11C20: Matrices, determinants [See also 15B36] 13F20: Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]

Frobenius problem polynomials arithmetic of function fields


Conceição, R.; Gondim, R.; Rodriguez, M. On a Frobenius problem for polynomials. Rocky Mountain J. Math. 47 (2017), no. 5, 1427--1462. doi:10.1216/RMJ-2017-47-5-1427.

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