OFFSET
1,2
COMMENTS
Not multiplicative; the smallest counterexample is a(63). - T. D. Noe, Nov 14 2006
REFERENCES
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.
LINKS
David W. Wilson, Table of n, a(n) for n=1..10000
Earle Blanton, Spencer Hurd and Judson McCranie, On the Digraph Defined by Squaring Modulo n, Fib. Quarterly, vol. 30, #4, 1992, 322-334.
J. J. Brennan and B. Geist, Analysis of Iterated Modular Exponentiation: The Orbits of x alpha mod N, Designs, Codes and Cryptography 13, 229-245 (1998) (specially Th. 6 and 7).
G. Chassé, Applications d'un corps fini dans lui-même, Publications mathématiques et informatique de Rennes, no. 4 (1985), p. 207-219; Math. Rev. 86e:11118.
Sean A. Irvine, Java program (github)
T. D. Rogers, The graph of the square mapping on the prime fields, Discrete Math. 148 (1996), 317-324.
FORMULA
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
MATHEMATICA
Table[Length[ConnectedComponents[Graph[Range[0, n-1], Table[UndirectedEdge[i, Mod[i^2, n]], {i, 0, n-1}]]]], {n, 100}] (* Keyang Li, Nov 04 2024 *)
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
STATUS
approved