prove $x^2 - x + 1$ divides $x^{10} - x^7 + x^4 + ax + b$ for some $a, b$ in an arbitrary field
9118
Polynomial division: an obvious trick? [reducing mod $\textit{simpler}$ multiples]
103817
Find splitting field of $x^5-4x+2$ over $\mathbb{Q}$
83662
Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$?
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
117167
$3^{n+1}$ divides $2^{3^n}+1$
100162
Minimal polynomial over an extension field divides the minimal polynomial over the base field
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
10548
The equation $-1 = x^2 + y^2$ in finite fields
124131
Show that $(x-1)^2$ is a factor of $x^n -nx +n-1$
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
113359
Proving that $x^2 + 4$ is not divisible by $3$
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
10111
Prove or disprove that Q[√2] is a field
32391
Show that $x^2+x+4$ is irreducible over $\mathbb Z_{11}$.