2020
DOI: 10.1134/s2070046620010021
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Counting Fixed Points and Rooted Closed Walks of the Singular Map $$x \mapsto {x^{{x^n}}}$$ Modulo Powers of a Prime

Abstract: The "self-power" map x → x x modulo m and its generalized form x → x x n modulo m are of considerable interest for both theoretical reasons and for potential applications to cryptography. In this paper, we use p-adic methods, primarily p-adic interpolation, Hensel's lemma, and lifting singular points modulo p, to count fixed points and two-cycles of equations related to these maps when m is a prime power.

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