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

Abstract.The Frobenius number of a finite subset $A\subset \N$ such that $\gcd(A)=1$ is the largest integer which cannot be expressed as $\sum_{a\in A}ax_{a}$ with non-negative integers . We present an algorithm for the computation of . Without loss of generality we suppose that there exist $a,b\in A$ such that $\gcd(a,b)=1$ . We give a formula for in the particular case that for all $c,d\in A$ , can be written in the form with $x,y\geq 0$ (e.g. ). Using Euler polynomials we give a formula for in the case that $A=\{a,b,c\}$ .