# 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} }

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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