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Paper IPM / M / 7744  


Abstract:  
Let n be a positive integer and a be an integer.
Gauss proved that ∑_{dn}μ(n/d)a^{d} ≡ 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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