Arkiv för Matematik

, Volume 42, Issue 2, pp 301–306 | Cite as

Every positive integer is the Frobenius number of an irreducible numerical semigroup with at most four generators

  • Pedro A. García-Sánchez
  • José C. Rosales


Letg be a positive integer. We prove that there are positive integersn1,n2,n3 andn4 such that the semigroupS=(n1,n2,n3,n4) is an irreducible (symmetric or pseudosymmetric) numerical semigroup with g(S)=g.


Positive Integer Numerical Semigroup Frobenius Number Irreducible Numerical Semigroup 
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Copyright information

© Institut Mittag-Leffler 2004

Authors and Affiliations

  • Pedro A. García-Sánchez
    • 1
  • José C. Rosales
    • 2
  1. 1.Departamento de ÁlgebraUniversidad de GranadaGranadaSpain
  2. 2.Departamento de ÁlgebraUniversidad de GranadaGranadaSpain

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