Entry 118

If one has a palindromic quartic of form

$$z^4-abz^3+(a^2+b^2-2)z^2-abz+1=0$$ then its roots can be factored as roots $(x,y)$ of quadratics $$x^2+ax+1=0\\ y^2+by+1= 0$$ $$z = xy = \left(\tfrac{-a+\sqrt{a^2-4}}2\right) \left(\tfrac{-b+\sqrt{b^2-4}}2\right)$$ hence are products of quadratic units. (To be continued.)