Timeline for Elements of $\mathbb{F}_p$ represented by an irreducible polynomial $f(x) = x^3 +a_2 x^2 + a_1 x + a_0$, $f(x) \in \mathbb{F}_p[x]$

Current License: CC BY-SA 4.0

14 events

when toggle format	what		by	license	comment
Jun 21 at 21:49	history	edited	jjimenez	CC BY-SA 4.0	edited body
Jun 21 at 1:44	answer	added	Will Sawin		timeline score: 7
Jun 21 at 1:34	comment	added	jjimenez		Thank you Gerry. I will take a look at Lehmer’s paper.
Jun 21 at 1:18	comment	added	Gerry Myerson		Just to take a very special case, let $f(x)=x^3+a$ with $a$ not in $C$. Then the problem reduces to finding the number of $c$ in $C$ such that $c+a$ is in $a^iC$, $i=0,1,2$, and these numbers are the cyclotomic constants for the cubic case. Gauss worked them out in the Disquisitiones. They depend on the values of $r,s$ such that $p=r^2+3s^2$. See also msp.org/pjm/1955/5-1/pjm-v5-n1-p10-p.pdf (Emma Lehmer, On the number of solutions of $u^k+D=w^2\bmod p$, Pac J. Math 5 (1955) 103-118).
Jun 21 at 0:10	history	edited	jjimenez	CC BY-SA 4.0	added 1 character in body
Jun 21 at 0:10	history	edited	jjimenez	CC BY-SA 4.0	added 149 characters in body
Jun 20 at 23:21	history	edited	jjimenez	CC BY-SA 4.0	edited title
Jun 20 at 23:21	history	edited	jjimenez	CC BY-SA 4.0	deleted 1 character in body; edited title
Jun 20 at 22:34	comment	added	Chris Wuthrich		Your notation $\mathbb{Z}_p$ is probably not the $p$-adic integers, but $\mathbb{Z}/p\mathbb{Z}$.
Jun 20 at 22:04	history	edited	jjimenez	CC BY-SA 4.0	edited title
Jun 20 at 21:26	history	edited	jjimenez	CC BY-SA 4.0	deleted 1 character in body
Jun 20 at 21:26	history	edited	jjimenez	CC BY-SA 4.0	deleted 2 characters in body
S Jun 20 at 19:57	review	First questions
Jun 20 at 22:52
S Jun 20 at 19:57	history	asked	jjimenez	CC BY-SA 4.0