query: Why are the elements of GF(q), whose characteristic is 2, all squares?
positive_passages.docid: 23712
positive_passages.text: $F$ is a finite field of size $s$. Prove that if $s=2^m$ for some $m>0$, then all elements of F have a square root.
negative_passages.docid: 37677
negative_passages.text: Radical of $\mathfrak{gl}_n$
negative_passages.docid: 4228
negative_passages.text: Prove that the only automorphism of $\mathbb{Q}(\sqrt[3]{2})$ is the identity automorphism.
negative_passages.docid: 46565
negative_passages.text: Show that $\mathbb{Q}(\sqrt{2})$ is a field.
negative_passages.docid: 120498
negative_passages.text: Why perfect square has odd number of factors
negative_passages.docid: 73713
negative_passages.text: Prove that $\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})})$ is Galois over $\mathbb{Q}$ is Galois and determine the Galois group
negative_passages.docid: 92672
negative_passages.text: Number of elements which are cubes/higher powers in a finite field.
negative_passages.docid: 65224
negative_passages.text: Prove that if $a^2 = a$ for all elements of the ring $R$, then $R$ has characteristic 2. Is the converse of the statement true?
negative_passages.docid: 104300
negative_passages.text: Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
negative_passages.docid: 35216
negative_passages.text: Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension
negative_passages.docid: 108550
negative_passages.text: Elements of $\mathbb Q(2^{1/3})$
negative_passages.docid: 35660
negative_passages.text: Elements of order 2 in $D_{2n}$
negative_passages.docid: 32760
negative_passages.text: Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?
negative_passages.docid: 10548
negative_passages.text: The equation $-1 = x^2 + y^2$ in finite fields
negative_passages.docid: 134840
negative_passages.text: Generators and relations for $\text{PSL}(2, \mathbb{F}_q)$
negative_passages.docid: 107821
negative_passages.text: The ring of integers of $\mathbf{Q}[i]$
negative_passages.docid: 94296
negative_passages.text: Classifying the factor group $(\mathbb{Z} \times \mathbb{Z})/\langle (2, 2) \rangle$