$x^p - t$ has no roots in $\mathbb{F}_p(t)[x]$
121076
Show $x^p-t$ has no root in the field $\mathbb{F}_p(t)$
27494
$P_n(x):=1+ \sum_{m=1}^n\dfrac{x^m}{m!}$ has no real root for even $n$ and exactly one real root for odd $n$
37015
Prove $\int_X |f|^p=p\int^{\infty}_{0} t^{p-1}\mu({x: |f(x)>t}) dt\,$
30511
Monic $f(x)\in\Bbb Z[x]$ has no rational root if $f(0)\ \&\ f(1)$ odd [Parity Root Test, Modular Root Test]
124460
Show that if $f \in \mathbb{C} \left[x_1, \dots, x_n \right]$ vanishes at every point of $\mathbb{Z}^n$, then $f$ is the zero polynomial.
10627
When is $X^n-a$ is irreducible over F?
41173
If $f\in S_\infty$ and $\int_{\mathbb{R}}x^pf(x)d\mu=0$ for all $p\in\mathbb{N}$ then $f\equiv 0$?
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
134068
When polynomials f(x) and f'(x) are relatively prime, f(x) has no repeated roots. Why?
48906
Prove that T is diagonalizable if and only if the minimal polynomial of T has no repeated roots.
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
85383
No. Of real roots of an equation
134701
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$
54875
How to prove polynomials with degree $n$ does not form a vector space?
147325
Proving that if $f(x)=x$ has no real solution then $f(f(x))=x$ has no real solution either
92599
Prove there generally is no isomorphism between $R[x]/(x^2-a)$ and $R^2$