Morton, Patrick2020-09-172020-09-172019Morton, P. (2019). Solutions of diophantine equations as periodic points of p-adic algebraic f...: Discovery Service (IUPUI). New York Journal of Mathematics. http://arxiv.org/abs/1806.11079https://hdl.handle.net/1805/23866In this part we show that the diophantine equation X5+Y5=ε5(1−X5Y5) , where ε=−1+5√2 , has solutions in specific abelian extensions of quadratic fields K=Q(−d−−−√) in which −d≡±1 (mod 5 ). The coordinates of these solutions are values of the Rogers-Ramanujan continued fraction r(τ) , and are shown to be periodic points of an algebraic function.enPublisher Policydiophantine equationsThe Rogers-Ramanujan continued fractionalgebraic functionArticle