State Transition Diagrams for Modular Powers

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Each point represents an integer, joined to the point representing the result of the modular power. The structure of the final "state transition diagram" varies greatly with both the multiplier and modulus.

Contributed by: Stephen Wolfram (March 2011)
Based on a suggestion by: Stan Wagon
With additional contributions by Robert Baillie
Open content licensed under CC BY-NC-SA


Snapshots


Details

Mouse over points to see the integers to which they correspond. A number pointing to means the number has no root for the given .

Fermat's little theorem, Euler's theorem, quadratic residues and nonresidues, and other number theoretic phenomena are visible.



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