Showing that$(\vec{a}+\vec{b})\cdot[(\vec{b}+\vec{c})\times(\vec{c}+\vec{a})]=2\vec{a}\cdot(\vec{b}\times\vec{c})$
61666
Proving $ [(\vec{a}+\vec{b})\times(\vec{b}+\vec{c})]\cdot(\vec{c}+\vec{a})=2\vec{c}\cdot(\vec{b}\times\vec{a})$
9140
Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$
66404
Prove that:$\int_{a}^{b} f(x) dx = b \cdot f(b) - a \cdot f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) dx$
142028
If $\vec{a},\vec{b},\vec{c},\vec{d}$are unit vectors, $(\vec{a}\times\vec{b}).(\vec{c}\times\vec{d})=1$ and $\vec{a}.\vec{c}=\frac{1}{2}$,then
76267
Prove that: $x_1\cdot x_2\cdots x_n>y_1\cdot y_2\cdots y_m$.
18023
The direct sum $\oplus$ versus the cartesian product $\times$
61066
Prove: $(A\rightarrow B),(A\rightarrow C)\rightarrow B, \mapsto_{HPC} B $
55031
Show any matrix $A_{n\times n}$ can be written as sum of two nonsingular matrices
8554
Proof: $\mathrm{adj}(\mathrm{adj}(A)) = (\mathrm{det}(A))^{n-2} \cdot A$ for $A \in \mathbb{R}^{n\times n}$
73191
Proving that $\frac{1}{1\cdot 2} + \frac{1}{2\cdot 3} + \frac{1}{3 \cdot 4} +\ldots + \frac{1}{n(n+1)} = \frac{n}{n+1}$
14986
Proving a combinatorics equality: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$
57418
How to prove this statement: $\binom{r}{r}+\binom{r+1}{r}+\cdots+\binom{n}{r}=\binom{n+1}{r+1}$
150738
Proof of $(A - B) - C = A - (B \cup C)$
35777
$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
19656
Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination.
25648
Prove $(a_1+b_1)^{1/n}\cdots(a_n+b_n)^{1/n}\ge \left(a_1\cdots a_n\right)^{1/n}+\left(b_1\cdots b_n\right)^{1/n}$
154698
Union of Cartesian products: $X \times (Y \cup Z)= (X \times Y) \cup(X\times Z)$