A note on the fundamental theorem of algebra for the octonions

This paper is a revision of a portion of the authorʹs doctoral dissertation submitted to the University of Oregon. Using elementary concepts of K-theory, the Brouwer degree of the power map in the octonions is computed. Later, a proof of a weaker version of the fundamental theorem of algebra for polynomials with coefficients in the octonions is given. As a partial complement, a lower bound to the number of solutions of a homogeneous monomial equation over the octonions is obtained.