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