Geodesic
A Congruence for a Class of Arithmetic Functions
Canadian mathematical bulletin, Tome 9 (1966) no. 5, pp. 571-574

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There is considerable literature concerning the century old result that for arbitrary positive integers a and m, 1.1 where μ(m) is the usual Mobius function. For earlier work on this we refer to L.E. Dickson [4, pp. 84–86] and L. Carlitz [1,2]. Another reference not noted by the above authors is R. Vaidyanathaswamy [6], who noted that the left member of (1.1) represents the number of special fixed points of the m th power of a rational transformation of the n th degree. 
Subbarao, M.V. A Congruence for a Class of Arithmetic Functions. Canadian mathematical bulletin, Tome 9 (1966) no. 5, pp. 571-574. doi: 10.4153/CMB-1966-070-4
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