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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.
Contributed by:
Stephen Wolfram
Based on a suggestion by:
Stan Wagon
With additional contributions by Robert Baillie
THINGS TO TRY
Slider Zoom
Automatic Animation
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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.
RELATED LINKS
State Networks for Systems of Limited Size
(
NKS|Online
)
Systems of Limited Size and Class 2 Behavior
(
NKS|Online
)
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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