The graph of the square mapping on the prime fields

@article{Rogers1996TheGO,
  title={The graph of the square mapping on the prime fields},
  author={T. D. Rogers},
  journal={Discret. Math.},
  year={1996},
  volume={148},
  pages={317-324}
}
  • T. D. Rogers
  • Published 1996
  • Computer Science, Mathematics
  • Discret. Math.
Abstract The action of the quadratic map f ( x ) = x 2 on the multiplicative groups F p ∗ of the prime fields is examined in terms of an associated directed graph that sends an edge from each element to its image. A formula is given for the decomposition of the graph into cyclic components and their attached trees. The number of components c ( p ) (called the connectivity of the prime p ) is shown to take on certain values, assuming various hypotheses. 

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References

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Elementary Theory of Numbers
Applied abstract algebra
The Book of Prime Number Records
Basic Algebra I
Groups, Graphs, and Fermat's Last Theorem