Patrick Morton, Şerban Raianu
Abstract
It is shown that $c = -29/16$ is the unique rational number with smallest denominator, and the unique rational number of smallest numerator, for which the map $f(x) = x^2 + c$ has a rational cycle with period $3$. Several arithmetic conditions on the set of all such rational numbers $c$ are proved.
A significance statement is not available in the OpenAlex record.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
It is shown that $c = -29/16$ is the unique rational number with smallest denominator, and the unique rational number of smallest numerator, for which the map $f(x) = x^2 + c$ has a rational cycle with period $3$. Several arithmetic conditions on the set of all such rational numbers $c$ are proved.
Key concepts: Rational number, Mathematics, Quadratic equation, Property (philosophy), Set (abstract data type), Combinatorics, Discrete mathematics, Arithmetic