2-Variable Frobenius Problem in Z[\sqrt M]
Doyon Kim
TL;DR
This paper provides a formulaic solution to the 2-variable Frobenius problem in the ring Z[√m], where m is a positive non-square integer, extending understanding of Frobenius problems in quadratic integer rings.
Contribution
It introduces a formulaic solution specifically for the 2-variable Frobenius problem in Z[√m], a novel approach in quadratic integer rings.
Findings
Derived a formula for the Frobenius problem in Z[√m]
Extended Frobenius problem solutions to quadratic integer rings
Provided explicit solutions for the first kind of Frobenius problem
Abstract
Suppose that m is a positive integer, not a perfect square. We present a formula solution to the 2-variable Frobenius problem in Z[\sqrt m] of the "first kind" ([3]).
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Taxonomy
TopicsCommutative Algebra and Its Applications · Tensor decomposition and applications · Finite Group Theory Research