Primitive elements on lines in extensions of finite fields
Stephen D. Cohen · Contemporary mathematics - American Mathematical Society · 2010
Given an integer n > 1, for which prime powers q does every translate {0 + a : a is an element of F-q} (with F-q(theta) = F(q)n) contain a primitive element of F(q)n? Further, for which prime powers does every line {alpha(0 + a) : a is an element of F-q} (with F-q(theta) = F(q)n and alpha (not equal 0) is an element of F(q)n) contain a primitive element? This paper incorporates a review of explicit results for n <= 4.