# Rational 6-cycles under iteration of quadratic polynomials

@article{Stoll2008Rational6U,
title={Rational 6-cycles under iteration of quadratic polynomials},
author={Michael Stoll},
journal={arXiv: Number Theory},
year={2008}
}
• M. Stoll
• Published 19 March 2008
• Mathematics
• arXiv: Number Theory
We present a proof, which is conditional on the Birch and Swinnerton-Dyer Conjecture for a specific abelian variety, that there do not exist rational numbers x and c such that x has exact period N = 6 under the iteration x |-> x^2 + c. This extends earlier results by Morton for N = 4 and by Flynn, Poonen and Schaefer for N = 5.
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