Solutions of diophantine equations as periodic points of $p$-adic algebraic functions, II: The Rogers-Ramanujan continued fraction

Patrick Morton

In this part we show that the diophantine equation $X^5+Y^5={\epsilon }^5(1-X^5{Y}^5)$, where $\epsilon =\frac{-1+\sqrt{5}}{2}$, has solutions in specific abelian extensions of qua…