query: Square root of $-1$ over a finite field
positive_passages.docid: 19968
positive_passages.text: Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
negative_passages.docid: 622
negative_passages.text: Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$
negative_passages.docid: 77820
negative_passages.text: Roots in a polynomial ring
negative_passages.docid: 65459
negative_passages.text: Roots of polynomials in field of prime characteristic p
negative_passages.docid: 120215
negative_passages.text: Sum of elements of a finite field
negative_passages.docid: 7954
negative_passages.text: Roots of monic polynomial over a number ring
negative_passages.docid: 144042
negative_passages.text: On the functional square root of $x^2+1$
negative_passages.docid: 10548
negative_passages.text: The equation $-1 = x^2 + y^2$ in finite fields
negative_passages.docid: 129755
negative_passages.text: Weighted sum of squares, in a finite field
negative_passages.docid: 42677
negative_passages.text: Proving $(\alpha + \beta)^{p^n} = \alpha^{p^n} + \beta^{p^n}$ in a finite field
negative_passages.docid: 60057
negative_passages.text: number of quadratic residues in finite field
negative_passages.docid: 117005
negative_passages.text: Rules in the ring with coefficients in finite field $\mathbb{F}_p$
negative_passages.docid: 3703
negative_passages.text: Order of finite fields is $p^n$
negative_passages.docid: 81875
negative_passages.text: why is $\sqrt{-1} = i$ and not $\pm i$?
negative_passages.docid: 69935
negative_passages.text: Field extensions of finite degree and primitive elements
negative_passages.docid: 3955
negative_passages.text: Square roots -- positive and negative
negative_passages.docid: 14633
negative_passages.text: What's the thing with $\sqrt{-1} = i$