Editing Normal basis (section)

== Primitive normal basis ==
A '''primitive normal basis''' of an extension of finite fields {{nowrap|''E'' / ''F''}} is a normal basis for {{nowrap|''E'' / ''F''}} that is generated by a [[Primitive element (finite field)|primitive element]] of ''E'', that is a generator of the multiplicative group ''K''<sup>×</sup>. (Note that this is a more restrictive definition of primitive element than that mentioned above after the general normal basis theorem: one requires powers of the element to produce every non-zero element of ''K'', not merely a basis.)  Lenstra and Schoof (1987) proved that every extension of finite fields possesses a primitive normal basis, the case when ''F'' is a [[prime field]] having been settled by [[Harold Davenport]].