$A$ nilpotent and $A+c_iB$ is nilpotent then $B$ is nilpotent.
125299
If A+tB is nilpotent for n+1 distinct values of t, then A and B are nilpotent.
34183
An equivalent condition with $\{0\}$ being the only nilpotent ideal
12596
Show that $f(x)=a_0+a_1x+a_2x^2+\cdots+a_nx^n\in R[x]$ is nilpotent iff $a_0,a_1,a_2,\ldots,a_n$ are nilpotent
63882
Show that the heisenberg group is nilpotent
1973
Traces of all positive powers of a matrix are zero implies it is nilpotent
5758
Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C
23869
Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive
42528
Prove that every idempotent element is not nilpotent element.
156443
if $x$ and $y$ commute with $[x y]$, then $[x y]$ is nilpotent
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
28460
Show matrix is nilpotent
56878
Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $
50266
In the following figure prove that: $AK||BC$
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
107128
Let $B$ be a nilpotent $n\times n$ matrix with complex entries let $A = B-I$ then find $\det(A)$