[GAP Forum] An Equation over a finite filed involving one of the primitive elements.

[Bulutoglu Dursun A Civ AFIT/ENC]

	Dear Gap Forum,
	I would like to first thank you for your help before.
	Now I am trying to solve the following problem:
	
	Let x be a primitive element of GF(p^n)  for n>=0.
	Then x can not satisfy an equation of the form:
	
x^r-A((p^n-1)/4)x+A((p^n-1)/4)-1=0  where 0=<r=<p^n-1 and 
A is a non-zero constant in GF(p^n).

Observe that r=0 or r=p^n-1 implies x=1. I would greatly appreciate it
if someone could give me an insight how this problem could be solved.	
Dursun.