A completely normal element of a finite field extension 
is an element 
that generates a normal basis over every intermediate
field. Equivalently, for each divisor 
of 
, the elements 
form a vector
basis over 
(Morgan and Mullen 1996).
Primitivity additionally requires 
to generate the multiplicative
group 
.
The Morgan-Mullen conjecture asserts
that these two requirements can always be met simultaneously.
