Prove $f$ is a unit in $A[X]\implies a_0$ is a unit in A and $a_1, . . . , a_n$ are nilpotent.
35222
Characterizing units in polynomial rings
31522
Proving $f$ has at least one zero inside unit disk
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
19884
The units of $\mathbb Z_4[x]$
145397
How to prove that for every $i$, $a_i = i$
68781
proving if $a \le b$ then $\sup(A) \le \inf(B)$
83798
Does $A$ a UFD imply that  $A[T]$ is also a UFD?
138026
To show that $n!f(x) \in \mathbb{Z}[x]$
117508
Prove that the closed unit ball of $L^2[a,b]$ is closed in $L^1[a,b]$
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
30860
Prove that $f(x)=0$ in $[-1,1]$.
133758
Traces of powers of a matrix $A$ over an algebra are zero implies $A$ nilpotent.
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
25748
If $G / Z(G)$ nilpotent then G is nilpotent.
32929
Questions about proving $\lnot \lnot a = a$
126821
Let $f:[0,1]\to \mathbb{R}$. Show that $\{a \in [0,1]: f(a)\neq 0\} = \bigcup_{n=1}^{\infty} \{a \in [0,1]: |f(a)|\geq 1/n\}$
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$