Prove that if $F$ is a finite field having q elements, then $a^{q-2}=a^{-1}$ for a nonzero $a \in F$
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
109647
Ext$_R^n(Q,A)=0=$Tor$_n^R(Q,A)$ where $Q$ is the field of fractions of a domain $R$
3703
Order of finite fields is $p^n$
157711
Number Theory: Prove that $m | \phi(a^m - 1)$
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
31917
If $q$ is coprime to $a$ then $a\mid nq-1,\,$ so $q$ is invertible mod $a$
41895
Show $\text{Hom}_{Ab}(A,\mathbb{Q}) = \{0\}$ for finite $A$
145140
Subfield of $\mathbb{Q}(\sqrt[n]{a})$
14918
Degree of splitting field of $X^n-1$ over some finite field
139499
The algebraic closure of a finite field and its Galois group
46951
For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$?
116594
Finite fields are isomorphic
115583
prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$
73454
Prove that $f$ has finite number of roots
73652
Exhibiting an isomorphism between two finite fields
81221
The prime number theorem over a finite field - Lang's *Algebra*, Chapter V, Exercise 23(b)