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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, 141-168 p.Article 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, 141-168 p.
Keyword [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: 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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