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On the fixed points of the map x→xx modulo a prime
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4734-5092
2015 (English)In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 22, no 1, p. 141-168Article in journal (Refereed) Published
Abstract [en]

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

Place, publisher, year, edition, pages
2015. Vol. 22, no 1, p. 141-168
Keywords [en]
Statistics, Residues, NN
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-166913ISI: 000353050500008Scopus ID: 2-s2.0-84927591623OAI: oai:DiVA.org:kth-166913DiVA, id: diva2:815312
Funder
Swedish Research CouncilKnut and Alice Wallenberg Foundation
Note

QC 20150529

Available from: 2015-05-29 Created: 2015-05-21 Last updated: 2017-12-04Bibliographically approved

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Kurlberg, Pär

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