A characterization of the Frobenius problem and its application to arithmetic progressions
Abstract
In the Frobenius problem we are given a set of coprime, positive integers a1, a2,...,ak, and are interested in the set of positive numbers NR that have no representation by the linear form Σi aixi in nonnegative integers x1, x2,...,xk. We give a functional relationship that completely characterizes the set NR, and apply it to the case when the numbers are in an arithmetic progression.
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