An extension of a result of Gauss to finite groups: a linear algebraic approach
نویسنده
چکیده
. Ist p eine Primzahl, so gilt für alle ganzen Zahlen a die Kongruenz a p ≡ a (mod p) (Folgerung aus dem Kleinen Fermatschen Satz). Mit der Eulerschen Phi-Funktion φ(n) gilt andererseits für beliebige teilerfremde ganze Zahlen n und a die Kongruenz aφ(n) ≡ 1 (mod n). 1797 begegnete der junge Gauss, in einem frühen Manuskript für ein nicht gedrucktes Schlusskapitel seiner Disquisitiones Arithmeticæ, im Spezialfall a prim der folgenden, für alle ganzen Zahlen a, n gültigen und heutzutage mit der Möbiusschen Funktion geschriebenen Kongruenz ∑
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