Does $x^2+1$ have roots in $Z_{103}[x]$?

Question

I am trying to figure out if $x^2+1$ has any roots in $Z_{103}[x]$, but I don't have any idea of how I should find the answer. Any help would be much appreciated. Thank you.

See http://math.stackexchange.com/questions/122048/1-is-a-quadratic-residue-modulo-p-if-and-only-if-p-equiv-1-pmod4 — lab bhattacharjee, May 29 '16 at 10:14

score 1 · Answer 1 · answered May 29 '16 at 10:16

1

No. Such a root cannot exist modulo $p$ when $p$ is one less than a multiple of $4$.

answered May 29 '16 at 10:16

Oscar Lanzi

48,208

Does $x^2+1$ have roots in $Z_{103}[x]$?

1 Answers1