Some contributions to the Frobenius’ Problem F. Aguil´ o-Gost 1,2 Dept. Matem` atica Aplicada IV Universitat Polit` ecnica de Catalunya Barcelona, Spain A. Miralles 1,3 Dept. Matem` atica Aplicada IV Universitat Polit` ecnica de Catalunya Castelldefels, Spain M. Zaragoz´ a 1,4 Dept. Matem` atica Aplicada IV Universitat Polit` ecnica de Catalunya Vilanova i la Geltr´ u, Spain Abstract Given a set A = {a 1 , ..., a k } with 1 ≤ a 1 < ... < a k and gcd(a 1 , ..., a k ) = 1, let us denote R(A)= {m ∈ N|∃λ 1 , ..., λ k ∈ N : m = k  i=1 λ i a i } and R(A)= N \R(A). The classical study of the Frobenius’ Problem for a given set A is the computation of the number f (A) = max R(A) (also called the Frobenius Electronic Notes in Discrete Mathematics 28 (2007) 61–68 1571-0653/$ – see front matter © 2007 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm doi:10.1016/j.endm.2007.01.010