Piotr Semenov
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 Dec 9 comment For $f(x) \in \mathcal{F}_{q^r}[x]$, how to find all $p(x)f(x)$ s.t. its coefficients are $\mathcal{F}_q$-linear over coefficients of $f(x)$? @JyrkiLahtonen So all the $p(x)$ that I want are only $\mathcal{F}_q[x]$? How it can be proven that there are no $p(x) \in \mathcal{F}_{q^r}[x] \setminus \mathcal{F}_q[x]$ satisfying my requirements? Dec 8 revised For $f(x) \in \mathcal{F}_{q^r}[x]$, how to find all $p(x)f(x)$ s.t. its coefficients are $\mathcal{F}_q$-linear over coefficients of $f(x)$? Improves the questions. Adds some details. Dec 8 revised For $f(x) \in \mathcal{F}_{q^r}[x]$, how to find all $p(x)f(x)$ s.t. its coefficients are $\mathcal{F}_q$-linear over coefficients of $f(x)$? Improves the questions. Adds some details. Dec 8 comment For $f(x) \in \mathcal{F}_{q^r}[x]$, how to find all $p(x)f(x)$ s.t. its coefficients are $\mathcal{F}_q$-linear over coefficients of $f(x)$? @JyrkiLahtonen: I mean that all the coefficients of $p(x)f(x) = \sum_i b_i \cdot x^i$ are the $\mathcal{F}_q$-linear combinations of coefficients of $f(x) = \sum_i a_i \cdot x^i$. In another words, each $b_i = \sum_j c_j \cdot a_j$, where $c_j \in \mathcal{F}_q$. Dec 8 asked For $f(x) \in \mathcal{F}_{q^r}[x]$, how to find all $p(x)f(x)$ s.t. its coefficients are $\mathcal{F}_q$-linear over coefficients of $f(x)$? Nov 30 revised Given the roots of polynomial over finite field, what is the count of its distinct nonzero coefficients? Detailed example is added. Nov 26 revised Given the roots of polynomial over finite field, what is the count of its distinct nonzero coefficients? Adds a special case I am interested in Nov 26 comment Given the roots of polynomial over finite field, what is the count of its distinct nonzero coefficients? @RobertIsrael: I have no assumptions about the finite field. It can be any $GF(q^p)$ for any prime $q$ and positive $p$. Nov 26 revised Given the roots of polynomial over finite field, what is the count of its distinct nonzero coefficients? added 34 characters in body Nov 26 revised Given the roots of polynomial over finite field, what is the count of its distinct nonzero coefficients? added 15 characters in body Nov 26 asked Given the roots of polynomial over finite field, what is the count of its distinct nonzero coefficients? Jun 22 awarded Popular Question Jun 3 awarded Yearling Dec 21 awarded Constituent Dec 17 awarded Caucus Feb 7 accepted How many ways to distribute $k$ indistinguishable balls over $m$ of $n$ distinguishable bins of finite capacity $l$? Feb 7 comment How many ways to distribute $k$ indistinguishable balls over $m$ of $n$ distinguishable bins of finite capacity $l$? sure, I specified the upper limit just to see the finite summation. Thank you for your answer! Feb 6 comment How many ways to distribute $k$ indistinguishable balls over $m$ of $n$ distinguishable bins of finite capacity $l$? Just to improve your answer, the upper limit of sum is $\lfloor \frac{k}{l} \rfloor-1$. Feb 6 comment How many ways to distribute $k$ indistinguishable balls over $m$ of $n$ distinguishable bins of finite capacity $l$? Just a small typo in your answer. Add $l$ balls to first bin, one have to distribute $k-l$ balls (instead of "$m-l$ units"). Feb 6 comment How many ways to distribute $k$ indistinguishable balls over $m$ of $n$ distinguishable bins of finite capacity $l$? Can you kindly explain, why $\binom{k-jl-1}{m-1}$ and not $\binom{k-jl-1}{m-j-1}$?