A good treatment have been given to the quaternion equations. Indeed, Ivan Niven in his paper Equations in Quaternion given in this link <http://jones.math.unibas.ch/~massierer/algebra-hs11/niven(quaternions).pdf> 
gave an algorithm on how to find all the solution of a given quaternion polynomial equation. Actually, in later papers the results were further improved.


Now my question is, is there similar treatment or even research about the polynomial equations over the octonions. I have searched google but I reached nothing. So, I thought someone would be able to help me.



The octonion equations
The paper


On Octonionic Polynomials
Rogério Serôdio (in advances in applied clifford algebras -- who knew such a journal existed?) seems to address precisely the questions you ask.


