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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Carlitz, L., An arithmetic function. Bull. Amer. Math. Soc. 43, (1937), pages 271-276. Google Scholar

[2] 2. Carlitz, L., Note on an arithmetic function. Amer. Math. Monthly, 59, (1952), pages 386-387. Google Scholar

[3] 3. Cashwell, E.D. and Everett, C.J., The ring of number theoretic functions. Pacific J. of Math. 9, (1959), pages 975-985. Google Scholar

[4] 4. Dickson, L.E., History of the Theory of Numbers. Vol. I. Google Scholar

[5] 5. McCarthy, P.J., On an arithmetic function. Monatsh Math. 63, (1959), pages 228-230. Google Scholar

[6] 6. Vaidyanathaswamy, R., Collected papers. Madras University. Google Scholar

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