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State Transition Diagrams for Modular Powers

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.

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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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PERMANENT CITATION

"State Transition Diagrams for Modular Powers" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/StateTransitionDiagramsForModularPowers/
Contributed by: Stephen Wolfram
Based on a suggestion by: Stan Wagon
With additional contributions by Robert Baillie
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