If $\mathbb{H}$ is a finite field and $a\neq0, b\neq0$, are elements of $\mathbb{H}$ then exists $u,v\in\mathbb{H}$ such that $1+au^{2}+bv^{2}=0 $
129755
Weighted sum of squares, in a finite field
69935
Field extensions of finite degree and primitive elements
108550
Elements of $\mathbb Q(2^{1/3})$
138212
Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$
82953
In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
14343
Every nonzero element in a finite ring is either a unit or a zero divisor
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
47041
What are the conditions for integers $D_1$ and $D_2$ so that $\mathbb{Q}[\sqrt {D_1}] \simeq \mathbb{Q}[\sqrt {D_2}]$ as fields.
42677
Proving $(\alpha + \beta)^{p^n} = \alpha^{p^n} + \beta^{p^n}$ in a finite field
144394
Order 2 elements in finite characteristic field
6984
Inverting $a+b\sqrt{2}$ in the field $\Bbb Q(\sqrt{2})$
78143
Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
133019
Nilpotent elements in $\mathbb Z_n$
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
143451
Homomorphism from $(\Bbb Q,+)$ to a finite group
46565
Show that $\mathbb{Q}(\sqrt{2})$ is a field.
26055
Multiplication by $0$ in a field