Find all $k$ such that $x^p+k$ is reducible over $\mathbb{Z}$.
4706
Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm)
13083
If for a polynomial $P(k) = 2^k$ for $k = 0, 1, . . . , n$, what is $P(n+1)$?
103238
Conjugates of ${\sqrt 5 + \sqrt 6 }$ over $\mathbb{Q}$ and irreducibility of $x^4 -22x^2+1$ (for minimal polynomial)
38876
$r! \equiv (−1)^k \pmod p$
18053
Find all prime $p$ such that $x^2=-1$ has a solution in $\mathbb{Z}/p\mathbb{Z}$
32391
Show that $x^2+x+4$ is irreducible over $\mathbb Z_{11}$.
76640
Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$
99453
Sum of $k$-th powers
61550
Existence of elements of order $p^k$ in a finite group
75166
Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$
29811
Find all polynomials $P$ such that $P(x^2+1)=P(x)^2+1$
10885
Existence of irreducible polynomials over finite field
131551
$pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
77620
Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $
63129
Infinite number of $k$ satisfying $p_{k+1} - p_{k} > 2$?