Panraksa C.Mahidol University2023-06-182023-06-182022-06-01International Journal of Number Theory Vol.18 No.5 (2022) , 1111-112917930421https://repository.li.mahidol.ac.th/handle/20.500.14594/85112In this paper, we study rational periodic points of polynomial fd,c(x) = xd + c over the field of rational numbers, where d is an integer greater than two. For period two, we describe periodic points for degrees d = 4, 6. We also demonstrate the nonexistence of rational periodic points of exact period two for d = 2k such that 3|2k - 1 and k has a prime factor greater than three. Moreover, assuming the abc-conjecture, we prove that fd,c has no rational periodic point of exact period greater than one for sufficiently large integer d and c ≠ - 1.MathematicsArticleSCOPUS10.1142/S17930421225005802-s2.0-85120845821