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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.