Caroline Lucheta, Eli Miller, and Clifford Reiter, Digraphs From Powers Modulo p, The Fibonacci Quarterly, 34 3 (1996) 226-239.

This paper investigates the structure of the digraphs that result from the iteration of xn modulo a prime p. One can show that cycles appear with a uniform binary tree structure attached to the cycle elements. The number of cycles of given order may be determined. The elements of any cycle have the same order and, thereby, there are direct connections between the geometry of the digraph and arithmetic properties of Z/pZ. Indeed, subgroups of the group correspond to elements of the digraph up to a given level. Some special cases where long cycles occur are considered.

See Also: · Paper [Preprint] · There is an established and growing literature related to this subject. A motivating reference was: E. L. Blanton, Jr, S. P. Hurd and J. S. McCranie, On a Digraph defined by squaring modulo n, The Fibonacci Quarterly 30 4 (1992) 322-334. · An investigation of general quadratic digraphs appears in [nt_2001].