Prove that in a ring with $x^3 = x$ we have $x+x+x+x+x+x=0$.
52454
If $x^3 =x$ then $6x=0$ in a ring
106305
Prove/disprove: if $\det(A+X) = \det(B + X)$ for all $X$, then $A=B$
156356
Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction
126427
Proving $\sqrt{2}+\sqrt[3]{3}$ is algebraic.
83100
Prove that the center of a ring is a subring.
49744
Find remainder of division of $x^3$ by $x^2-x+1$
14191
How many elements does the ring $ℤ[X]/(X^2-3,2X-4)$ have? Describe the structure of this ring.
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
99835
Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
112150
Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
41364
How to prove that $x^y - y^x = x + y$ has only one solution in positive integers?
73743
Number of elements in the quotient ring $\mathbb{Z}[X]/(X^2-3, 2X+4)$
61987
$x^2+1=0$ in $\mathbb{Z}_7$
36906
Prove that $x^n+x^{-n} \in \mathbf{N}$ if $x+\frac1x \in \mathbf{N}$
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
82609
Ring such that $x^4=x$ for all $x$ is commutative
82953
In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$