  Define the $n$-th fibotomic polynomial to be the product of the monic
irredicible factors of the $n$-th Fibonacci polynomial which are not factors of
any Fibonacci polynomial of smaller degree. In this paper, we prove a number of
properties of the fibotomic polynomials. This includes determining the
discriminant of the fibotomic polynomials and the resultant of pairs of
fibotomic polynomials. Furthermore, we completely determine the factorization
form of the fibotomic polynomials in prime fields. Results are also generalized
for the bivariate homogenous fibotomic polynomials.

Number Theory