Let be two integers. Let be of degree and let be monic polynomials such that the sum of their degrees is .
The goal of this exercise is to show that all remainders can be computed in operations in .
The following result (proved in class) will be essential: division-with-remainder of a polynomial of degree by a monic polynomial of degree (where are non-negative integers) can be done in at most ring operations in where we have
Marc Moreno Maza