Morton, PatrickRaianu, Serban2023-11-012023-11-012022-11Morton, P., & Raianu, S. (2022). Arithmetic properties of 3-cycles of quadratic maps over Q. Journal of Number Theory, 240, 685–729. https://doi.org/10.1016/j.jnt.2022.01.005https://hdl.handle.net/1805/36851It is shown that c = -29/16 is the unique rational number of smallest denominator, and the unique rational number of smallest numerator, for which the map fc(x) = x2 + c has a rational periodic point of period 3. Several arithmetic conditions on the set of all such rational numbers c and the rational orbits of fc(x) are proved. A graph on the numerators of the rational 3-periodic points of maps fc is considered which reflects connections between solutions of norm equations from the cubic field of discriminant -23.en-USPublisher Policyarithmetic propertiesquadratic mapperiodic pointsrational orbitsrational numbersArticle