Walde, Ralph; Russo, Paula Rational periodic points of the quadratic function \(Q_ c(x)=x^ 2+c\). (English) Zbl 0804.58036 Am. Math. Mon. 101, No. 4, 318-331 (1994). A condition for the existence of rational fixed points and periodic points (of periods 2 and 3) for \(Q_ c(x) = x^ 2 + c\) depending on \(c\) is given (also a condition for nonexistence of rational periodic points of higher periods). There is a connection to Pythagorean triples and some results on periodic points of \(Q_ c\) treated as a function over \(p\)-adic numbers. Reviewer: T.Nowicki (Warszawa) Cited in 1 ReviewCited in 21 Documents MSC: 37P05 Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps 11R09 Polynomials (irreducibility, etc.) 37P45 Families and moduli spaces in arithmetic and non-Archimedean dynamical systems Keywords:quadratic function; \(p\)-adic numbers; periodic points PDFBibTeX XMLCite \textit{R. Walde} and \textit{P. Russo}, Am. Math. Mon. 101, No. 4, 318--331 (1994; Zbl 0804.58036) Full Text: DOI