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IPM
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“School of Mathematics”

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Paper   IPM / M / 7744
School of Mathematics
  Title:   An extension of a result of Gauss to finite groups: a linear algebraic approach
  Author(s):  M. R. Pournaki
  Status:   Published
  Journal: Elem. Math.
  Vol.:  61
  Year:  2006
  Pages:   24-31
  Supported by:  IPM
  Abstract:
Let n be a positive integer and a be an integer. Gauss proved that ∑d|nμ(n/d)ad ≡ 0 (mod n), where μ is the Mobius function. This result generalizes both Fermat's Little Theorem and Euler's Theorem. In this paper, a generalization of this result to finite groups is proved by methods of (multi-) linear algebra.

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