Suppose that $a$ and $b$ belong to a field of order $8$ and that $a^2 + ab + b^2 =0$ then $a=0$ and $b=0$ .
71608
A property of finite field of order $2^n$
151806
Prove that $A^k = 0 $ iff $A^2 = 0$
124995
$p\equiv 1,2,3\text{ mod }8 \Rightarrow p=a^2+2b^2\text{ for some $a,b\in\mathbb{Z}$.}$
9520
Subfields of $\Bbb Q(\zeta_8)$
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
23641
Quotient ring of field is zero or itself.
63280
Show that the set $\mathbb{Q}[\sqrt{2}] = \{a + b \sqrt{2} \mid a, b \in \mathbb{Q}\}$ is a field with the usual multiplication and addition.
43470
Prove: For odd integers $a$ and $b$, the equation $x^2 + 2 a x + 2 b = 0$ has no integer or rational roots.
139934
In $\mathbb{Z}/(n)$, does $(a) = (b)$ imply that $a$ and $b$ are associates?
67394
How to interpret $\mathbb{P}(B|A)$ when $\mathbb{P}(A) = 0$
10111
Prove or disprove that Q[√2] is a field
68389
Proving $ \frac{(a-b)^2}{8a}\leqslant\frac{a+b}{2} - \sqrt{ab} \leqslant\frac{(a-b)^2}{8b}$ when $ 0<b\le a$
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
34906
Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.
66451
In a ring, how do we prove that a * 0 = 0?
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
148343
The sum of the elements in a field of at least three elements is 0