A New Algorithm for Computing the Frobenius Number

2024/02/12 by Taheri, Abbas, Alikhani, Saeid
#01B39 #11D04 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2402.07853

Abstract

A number α has a representation with respect to the numbers α₁,...,α_n, if there exist the non-negative integers λ₁,... ,λ_n such that α=λ₁α₁+...+λ_n α_n. The largest natural number that does not have a representation with respect to the numbers α₁,...,α_n is called the Frobenius number and is denoted by the symbol g(α₁,...,α_n). In this paper, we present a new algorithm to calculate the Frobenius number. Also we present the sequential form of the new algorithm.

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