On Tue, February 7, 2017 10:21 am, Surinder Kaur wrote: > If F is a field with q = p^m -1 elements where m is even and p is an odd > prime,
Since the existence of a field F with q elements implies that q is a prime power and since for an odd prime p we have q = p^m - 1 even, we can conclude that q is in fact a power of 2, and that F has characteristic 2. > A the set of all quadratic residues and B = {4 b - 1 | b is > primitive element of F}. Since F has characteristic 2, we have B = {1}. > Then my aim is to prove A intersection B is non > empty i.e. for some primitive element b the element 4b-1 is a square of > some element. Just take any primitive element b. -- Then we have 4b-1 = 1 (since F has characteristic 2), and 1 is the square of itself. qed. -- Does this help you? Best regards, Stefan Kohl P.S.: The GAP Forum is intended for questions on GAP. -- General questions on mathematics are more on-topic on Math.SE. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum