Atsanon WadsanthatChatchawan PanraksaMahidol University2020-01-272020-01-272019-02-01Fibonacci Quarterly. Vol.57, No.1 (2019), 35-44001505172-s2.0-85063099200https://repository.li.mahidol.ac.th/handle/123456789/51230© 2019 Fibonacci Association. All Rights Reserved. The map x 7→ x 2 +x defined on a fixed finite field of characteristic 2 is investigated as a dynamical system. The map is known to be a linear map. Its nilpotent points form a subfield, and periodic cycles are somewhat uniform. A general upper bound for the cycle lengths is given in terms of the Carmichael function of the field degree.Mahidol UniversityMathematicsArticleSCOPUS