TY - JOUR
T1 - On the fixed points of the map x→xx modulo a prime
AU - Kurlberg, Pär
AU - Luca, Florian
AU - Shparlinski, Igor E.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84927591623&partnerID=8YFLogxK
U2 - 10.4310/MRL.2015.v22.n1.a8
DO - 10.4310/MRL.2015.v22.n1.a8
M3 - Article
AN - SCOPUS:84927591623
SN - 1073-2780
VL - 22
SP - 141
EP - 168
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 1
ER -