The Frobenius number corresponding to the squares of three consecutive Fibonacci numbers: comparison of three algorithmic processes

TL;DR

This paper computes the Frobenius number for semigroups generated by squares of three consecutive Fibonacci numbers, comparing three different algorithmic methods for efficiency and accuracy.

Contribution

It introduces a comparative analysis of three existing algorithms applied to a specific Fibonacci-based numerical semigroup problem.

Findings

All three algorithms successfully compute the Frobenius number.

The paper identifies the most efficient algorithm among the three.

Provides insights into the computational complexity of each method.

Abstract

We compute the Frobenius number for numerical semigroups generated by the squares of three consecutive Fibonacci numbers. We achieve this by using and comparing three distinct algorithmic approaches: those developed by Ram\'irez Alfons\'in and R{\o}dseth ([15]), Rosales and Garc\'ia-S\'anchez ([20]), and Tripathi ([26]).