Proof Enquiry, Field of order $p^n$
6855
Subfields of finite fields
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
125568
Construction of $p^n$ field
138083
$\gcd(X^n - 1, nX^{n-1}) = 1$ in a field $K$ of characteristic $0$ or characteristic $p \nmid n$.
4706
Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm)
151732
Number of solutions of polynomials in a field
61550
Existence of elements of order $p^k$ in a finite group
7843
Show that order of $a^k$
42332
Existence of multiplicative inverse in field $\mathbb{Q}(\sqrt{d})$
153123
Proving by induction $4^n  0$
157841
Existence of a non-abelian group of order $p^n$.
54369
Proof of $n^2 \leq 2^n$.
17178
Order of $\phi(g)$ divides the order of $g$
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
70129
Prove that in an ordered field $(1+x)^n \ge 1 + nx + \frac{n(n-1)}{2}x^2$ for $x \ge 0$
83752
If $p + q = 1$ prove that for any natural $n, m$ following is true: $(1 - p^n)^m + (1 - q^m)^n \ge 1$
46795
Explicit construction of a finite field with $p^n$ elements