# IJPAM: Volume 60, No. 1 (2010)

**COMPUTING THE FROBENIUS NUMBER**

Abdallah Badra

Laboratoire de Mathématiques

Université Blaise Pascal

Les Cézeaux, Aubière Cedex, 63177, FRANCE

e-mail: abdallah.badra@math.univ-bpclermont.fr

Laboratoire de Mathématiques

Université Blaise Pascal

Les Cézeaux, Aubière Cedex, 63177, FRANCE

e-mail: abdallah.badra@math.univ-bpclermont.fr

**Abstract.**The Frobenius number of a finite subset such that is the largest integer which cannot be expressed as
with non-negative integers . We present an algorithm for the computation of . Without loss of generality we suppose that there exist such that . We give a formula for in the particular case that for all , can be written in the form with (e.g. ). Using Euler polynomials we give a formula for in the case that .

**Received: **February 19, 2010

**AMS Subject Classification: **11D04

**Key Words and Phrases: **Frobenius number, linear Diophantine equation

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2010

**Volume:** 60

**Issue:** 1