In an integral domain prove that $a=b$
126280
In a P.I.D., if $a^m = b^m$ and $a^n = b^n$ for $m, n \in \mathbb{N}$ with $\gcd(m,n) = 1$, then $a=b$
125868
Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.
132193
Why $\Bbb Z$ = (integers) is an integral domain?
119156
$(a,b)=d \overset{?}{\implies} (a^3,b^3)=d^3$
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
20110
How to prove $(AB)^T=B^T A^T$
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
51321
Prove that $A = B = C = D$
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
150738
Proof of $(A - B) - C = A - (B \cup C)$
97184
Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $
69656
Prove or disprove that $\int_a^b |f(x)|\ \mathrm{d}x\geq \big | \int_a^b f(x)\ \mathrm{d}x\big| $
34398
Prove $\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$
62951
Is there a more direct way of proving that this ring is an integral domain?
131120
Proving an integral equation.
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
57669
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.