Exercise 15, § 11

Let $K$ be a Moriya field (Ex. 13) and $P$ the set of prime numbers dividing the degree of an algebraic extension of finite degree of $K$. Show that the set of degrees of algebraic extensions of finite degree of $K$ is either equal to the set $N$, of integers all of whose prime factors are in $P$ or to the subset of $N_P$ consisting of integers not divisible by 4.