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Paper   IPM / M / 13411
School of Mathematics
  Title:   Solving linear systems of equations over integers with Grobner bases
  Author(s):  A. Hashemi
  Status:   Published
  Journal: Acta Arith.
  Vol.:  163
  Year:  2014
  Pages:   261-270
  Supported by:  IPM
We introduce a novel application of Gröbner bases to solve (non-homogeneous) systems of integer linear equations over integers. For this purpose, we present a new algorithm which ascertains whether a linear system of equations has an integer solution or not; in the affirmative case, the general integer solution of the system is determined.

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