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 Yearling
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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
accepted What is the number of $0\leq j_1, j_2, \ldots, j_n\leq v-1$ such that $\sum_{i=1}^{n}j_i\equiv 0 \mod v$?
Feb
3
revised What is the number of $0\leq j_1, j_2, \ldots, j_n\leq v-1$ such that $\sum_{i=1}^{n}j_i\equiv 0 \mod v$?
What I tried is wrong so I removed it all together
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.
Feb
3
revised What is the number of $0\leq j_1, j_2, \ldots, j_n\leq v-1$ such that $\sum_{i=1}^{n}j_i\equiv 0 \mod v$?
added 60 characters in body
Feb
3
asked What is the number of $0\leq j_1, j_2, \ldots, j_n\leq v-1$ such that $\sum_{i=1}^{n}j_i\equiv 0 \mod v$?
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
16
accepted Finite fields: factorization of the trace function over the base field
Nov
12
revised Finite fields: factorization of the trace function over the base field
deleted 233 characters in body
Nov
12
revised Finite fields: factorization of the trace function over the base field
edited body
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.
Nov
12
asked Finite fields: factorization of the trace function over the base field
Jun
11
revised Can every periodic binary sequence be expressed as the output of a Linear or Non-Linear Feedback Shift Register?
added 2 characters in body
Jun
11
revised Can every periodic binary sequence be expressed as the output of a Linear or Non-Linear Feedback Shift Register?
added 2 characters in body
Apr
26
accepted Isomorphism of the annihilator of a subgroup in the context of group characters.
Apr
21
revised 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?
edited body
Apr
21
awarded  Yearling
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.