Numerische Mathematik

, Volume 34, Issue 4, pp 349–352 | Cite as

An algorithm for a linear diophantine equation and a problem of Frobenius

  • Harold Greenberg


We solve the diophantine equation\(\sum\limits_{j = 1}^n {a_j x_j } = L\) for nonnegative variablesx j , wherea j andL are positive integers. We characterize both the values ofL that lead to solutions and those that do not lead to solutions. We solve the Frobenius problem of finding the largest value ofL for which no solution exists.

Subject Classifications

AMS(MOS): 10B05 CR: 5.14 


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  1. 1.
    Heap, B.R., Lynn, M.S.: On a linear diophantine problem of Frobenius, an improved algorithm. Numer. Math.7, 226–231 (1965)Google Scholar
  2. 2.
    Selmer, E.S.: On the linear diophantine problem of probenius. J. Reine Angew. Math.293/294, 1–17 (1977)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Harold Greenberg
    • 1
  1. 1.Faculty of Social Sciences, Department of StatisticsTel-Aviv UniversityTel-AvivIsrael

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