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A023153
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Number of cycles of function f(x) = x^2 mod n.
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12
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1, 2, 2, 2, 2, 4, 3, 2, 3, 4, 3, 4, 3, 6, 4, 2, 2, 6, 4, 4, 6, 6, 3, 4, 3, 6, 4, 6, 4, 8, 6, 2, 6, 4, 6, 6, 4, 8, 6, 4, 3, 12, 7, 6, 6, 6, 4, 4, 7, 6, 4, 6, 3, 8, 6, 6, 8, 8, 3, 8, 6, 12, 10, 2, 6, 12, 6, 4, 6, 12, 7, 6, 4, 8, 6, 8, 10, 12, 6, 4, 5, 6, 4, 12, 4, 14, 8, 6, 3, 12, 10, 6, 12, 8, 8, 4, 3, 14, 10, 6
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OFFSET
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1,2
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COMMENTS
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Not multiplicative; the smallest counterexample is a(63). - T. D. Noe, Nov 14 2006
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REFERENCES
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Earle Blanton, Spencer Hurd and Judson McCranie, On the Digraph Defined by Squaring Mod m, When m Has Primitive Roots, Congressus Numerantium, vol. 82, 167-177, 1992.
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LINKS
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FORMULA
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In case (Z/nZ)^* is cyclic there is a formula (see Chasse and Rogers). Let C_m denote the cyclic group of order m. Let a(m) denote the number of cycles in the graph of C_m relative to the mapping f. Then the number of cycles equals a(m) = Sum_{d|n} phi(d)/ord_d(2). - Pieter Moree, Jul 04 2002
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CROSSREFS
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Cf. A023154-A023161 (cycles of the functions f(x)=x^k mod n for k=3..10).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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