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arXiv · 1402.4464

On the Fixed Points of the Map x -> x^x Modulo a Prime

Pär Kurlberg·Florian Luca·Igor Shparlinski
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Abstract

In this paper, we show that for almost all primes p there is an integer solution x in [2,p-1] to the congruence x^x == x mod p. The solutions can be interpretated as fixed points of the map x -> x^x mod p, and we study numerically and discuss some unexpected properties of the dynamical system associated with this map.

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Pär Kurlberg, Florian Luca, Igor Shparlinski. 2014-02-18. On the Fixed Points of the Map x -> x^x Modulo a Prime. https://arxiv.org/abs/1402.4464

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