Show that $e^A e^B=e^{A+B} e^{[A,B]/2}$?
116558
Consider two linear operators $\hat{A}$ and $\hat{B}$. Show that $e^{\hat{A}}e^{\hat{B}}=e^{\hat{A}+\hat{B}}e^{[\hat{A},\hat{B}]/2}$
115176
Can we say that $\left(a+b\right)^{\alpha}>a^{\alpha}+b^{\alpha}$ for all $a,b>0$ and $\alpha>1$?
127891
If $ a^{2} + b^{2} = c^{2}$ and $c$ is even, prove that $a$ and $b$ are both even.
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
87397
Show that $a^2 \bmod b = (a \bmod b)^2 \bmod b$
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
25907
Show $a\Bbb Z+b\Bbb Z = \gcd(a,b)\Bbb Z$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
52357
If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
32103
Show that for a $2\times 2$ matrix $A^2=0$
34275
How do I show that $\frac {a^2}b + \frac {b^2}c + \frac {c^2}d + \frac {d^2}a \ge 4$ for $a^2 + b^2 + c^2 + d^2 = 4$?
85449
Show a,b,c congruences when $a^2+b^2=c^2$
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
5729
If $a^2+b^2+c^2=1$ then prove the following.
89175
Proof of $(a+b)^{n+1}$