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seen Jul 9 at 17:39

Jul
9
accepted Which powers of a primitive element of a finite field yield a generator of a finite field extension?
Jul
7
comment Which powers of a primitive element of a finite field yield a generator of a finite field extension?
Thanks for your answer. Now, you say that WLOG, $i|(q^m-1)$, else $i$ is associate to a divisor's residue in $\Bbb{Z}_{q^m-1}$. Could you comment on that? I fail to understand it..
Jul
4
comment Which powers of a primitive element of a finite field yield a generator of a finite field extension?
Note that the last bullet is equivalent to "there is no $s$ such that $0<s<m$ and $\frac{q^m-1}{q-1}|i\frac{q^s-1}{q-1}$. So it follows that when $gcd(i,\frac{q^m-1}{q-1})=1$ this is true, but I couldn't prove that this is an if and only if condition
Jul
4
asked Which powers of a primitive element of a finite field yield a generator of a finite field extension?
Jul
2
awarded  Curious
Jun
28
awarded  Critic
Jun
27
accepted When is $c\alpha$ primitive, for nonzero $c\in GF(q)$ and $\alpha$ primitive in $GF(q^m)$?
Jun
27
revised When is $c\alpha$ primitive, for nonzero $c\in GF(q)$ and $\alpha$ primitive in $GF(q^m)$?
Inserted EDIT lines
Jun
27
asked When is $c\alpha$ primitive, for nonzero $c\in GF(q)$ and $\alpha$ primitive in $GF(q^m)$?
Jun
27
comment Order of product of two elements in a group
$m,n$ should be $mn$ but edits have to have at least 6 characters changes, so I cannot edit
May
9
asked What is the number of solutions that satisfy this gcd equation?
Apr
24
answered What is the definition of a non-degenerate homogeneous quadratic form over a finite field?
Apr
24
accepted What is the definition of a non-degenerate homogeneous quadratic form over a finite field?
Apr
24
asked What is the definition of a non-degenerate homogeneous quadratic form over a finite field?
Apr
12
accepted Linear independence of finite field elements and subfields
Apr
12
comment Linear independence of finite field elements and subfields
Thank you so much for the thorough answer, this is helpful.
Apr
12
comment Linear independence of finite field elements and subfields
Thanks Gerry, I should have been more careful. I updated the question.
Apr
12
revised Linear independence of finite field elements and subfields
added 62 characters in body
Apr
11
asked Linear independence of finite field elements and subfields
Apr
9
comment Generalization of a projective plane?
Thanks, Quiaochu! I'll try to understand now how this generalizes the definition of a projective plane.