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Feb
4
comment What is the number of $0\leq j_1, j_2, \ldots, j_n\leq v-1$ such that $\sum_{i=1}^{n}j_i\equiv 0 \mod v$?
Yup, should be quite easy. Maybe change a bit for n odd or even..
Feb
3
comment What is the number of $0\leq j_1, j_2, \ldots, j_n\leq v-1$ such that $\sum_{i=1}^{n}j_i\equiv 0 \mod v$?
Thanks! Using your answer here it was fairly simple to get a recursive formula: If $N_n$ is the number question (with the $j$'s being $>0$, then it seems that $N_n=(v-1)^{n-1} - N_{n-1}$. I did it a bit quickly but it should be right. From that I think I'll be able to get a formula.
Feb
3
comment What is the number of $0\leq j_1, j_2, \ldots, j_n\leq v-1$ such that $\sum_{i=1}^{n}j_i\equiv 0 \mod v$?
So, I was not careful again. In my original question I needed to put that $1 \leq \j_1, j_2, \ldots, j_n\leq v-1$. I accepted your answer because it is correct for the question I asked and may prove to be helpful to others. On top of that, I think I can work on a proof by using your idea. In particular, for the case $n=3$, we have $v^2$ tuples including the cases when any of $j_1,j_2,j_3$ are $0$, and then we subtract the cases that $j_1+j_2\equiv 0 \bmod v$. Then we end up having (v-1)(v-2). I think this should be an easy application of the inclusion-exclusion principle.. I'll work on it.
Feb
3
comment What is the number of $0\leq j_1, j_2, \ldots, j_n\leq v-1$ such that $\sum_{i=1}^{n}j_i\equiv 0 \mod v$?
@David Ooops, I meant for the case $n=3$. Corrected now, thank you.
Nov
16
comment Finite fields: factorization of the trace function over the base field
Jyrki and @Thomas: Thanks both of you for providing an answer. Jyrki, you have been answering a lot of my finite fields questions, thanks for all the help.
Nov
12
comment Finite fields: factorization of the trace function over the base field
@ThomasAndrews Your comments are all valid.. I'll modify the question to make more sense.
Apr
21
comment How can I construct the matrix representing a linear transformation of a 2x2 matrix to its transpose with respect to a given set of bases?
@ahorn That's a good point, Indeed my choice was arbitrary. I edited my answer to reflect this.
Mar
16
comment Finite field question involving the trace and a permutation.
Many thanks Jyrki, I'll need to study this a bit. I'll update later.
Mar
16
comment Finite field question involving the trace and a permutation.
I know a couple of people who were claiming that they could do math better after a couple of beers :) Anyway, I think I have an idea, but I have to double think before posting anything, I'm not sure yet.
Mar
10
comment Bijections of a finite field that preserve the kernel of the trace
I have realized what my $f(x)$ should be. Indeed, I was asking too much. If you want, check my updated question here: math.stackexchange.com/questions/1183155/…
Feb
24
comment Bijections of a finite field that preserve the kernel of the trace
Thank you for your clear and thorough answer, I was quite off with my conjecture about these monomials. I will have to think how/if the question can be restated to suggest some other class of polynomials.
Feb
24
comment Bijections of a finite field that preserve the kernel of the trace
I think I was being quite careless when I wrote that title. It should be just bijections.
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
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
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
9
comment Generalization of a projective plane?
Thanks, Quiaochu! I'll try to understand now how this generalizes the definition of a projective plane.
Apr
8
comment Generalization of a projective plane?
I can't create a tag, but I was wondering if it would make sense to have a "finite-geometry" tag.
Oct
26
comment Ordering compositions of integers, where cyclic shifts are not considered distinct
Please help me with the tags; I have < 300 reputation so I cannot create tags related to "integer compositions" "ordering", etc. Not sure what else to tag there.. Thank you.