I investigated about the generalizations of Fermat's little theorem and found several ones in the book of Dickson, History of the Theory of Numbers, Vol. 1, Carnegie Institution of Washington, Publication No. 256, 1919. Here the congruence $\sum_{dn}\mu(d)a^{n/d} \equiv 0\pmod n$ is a result from a posthumous paper of Gauss (1863) in a notation given by Gegenbauer (1900). The question is: Why and where is the reference that gives as author the name Ramachandra?
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