Timeline for Polynomial generated with primitive element modulo p

8 events

when toggle format	what		by	license	comment
May 27, 2015 at 6:55	history	edited	Angel del Rio	CC BY-SA 3.0	added 4 characters in body
Apr 14, 2015 at 16:27	comment	added	Angel del Rio		Another equivalent form of the question: Let $k\mod p$ denote the representative of $k$ modulo $p$ in the interval $[-n,n]$ where $n=\frac{p−1}{2}$. Consider the $n\times n$ matrix having $1$ in the $(i,j)$-th entry if $ij \mod p$ is odd and $0$ otherwise. Is A invertible in the ring of rational matrices?
Apr 8, 2015 at 12:53	comment	added	Gerry Myerson		The earlier post was mathoverflow.net/questions/202158/…
Apr 8, 2015 at 12:06	comment	added	Angel del Rio		I also verified using computers that for $p\le 1000$, $P(X)$ is of the form $X^k Q(X)$ with $Q(X)$ irreducible except for $p=223, 367, 727$ or $751$. In these four exceptions $P(X)=X^k Q(X) R(X)$, with $Q(X)$ and $R(X)$ irreducible and $Q$ either $X+1$ or $X^2+1$. Observe that in these exceptions $p\equiv -1 \mod 4$. It seems to me that there is some reason for this.
Apr 8, 2015 at 12:00	history	edited	Angel del Rio	CC BY-SA 3.0	[Edit removed during grace period]; added 1 character in body
S Apr 8, 2015 at 11:53	history	suggested	Oliver Braun	CC BY-SA 3.0	Fixed spelling in title.
Apr 8, 2015 at 11:45	review	Suggested edits
S Apr 8, 2015 at 11:53
Apr 8, 2015 at 10:15	history	asked	Angel del Rio	CC BY-SA 3.0