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On a Frobenius problem for polynomials. (English) Zbl 1431.11042

Summary: 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.

MSC:

11D07 The Frobenius problem
11C20 Matrices, determinants in number theory
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
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