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10:39 AM
What tag should be used for: Cubic polynomials over finite fields whose roots are quadratic residues or non-residues? (The question has no top-level tag and one deprecated tag.)
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Q: Cubic polynomials over finite fields whose roots are quadratic residues or non-residues

FranzNietzscheFor a cubic polynomial $f(x)=x^3+x^2+\frac{1}{4}x+c$ over $\mathbb{F}_q$, where $q$ is a odd prime power, I find that for a lot of $q$, there does not exist $c\in\mathbb{F}_q$ such that $f$ has three distinct roots in $\mathbb{F}_q$, one of which is a quadratic residue and the other two are non-r...

I will point out that the tag (abstract-algebra) is deprecated on MO, see the tag-info. Also, it is recommended to use at least on of the top-level tags. — Martin Sleziak 14 secs ago
 
6 hours later…
4:21 PM
The tags have been edited by several users: mathoverflow.net/posts/349039/revisions
5
Q: Cubic polynomials over finite fields whose roots are quadratic residues or non-residues

FranzNietzscheFor a cubic polynomial $f(x)=x^3+x^2+\frac{1}{4}x+c$ over $\mathbb{F}_q$, where $q$ is a odd prime power, I find that for a lot of $q$, there does not exist $c\in\mathbb{F}_q$ such that $f$ has three distinct roots in $\mathbb{F}_q$, one of which is a quadratic residue and the other two are non-r...


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