$(x_1,\ldots x_n)=(1)\implies (x_1^{k_1},\ldots, x^{k_n})=(1)$
92822
Finite number of elements generating the unit ideal of a commutative ring
145397
How to prove that for every $i$, $a_i = i$
115459
Proving this $F_{n+1} \cdot F_{n-1} - F^2_n = (-1)^n$ by induction
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
27901
Proving $\sum\limits_{i=1}^k | \langle x,v_i \rangle \langle y,v_i\rangle| \leq \|x\|\cdot \|y\|$
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] $
75614
Proving that $n|m\implies f_n|f_m$
47670
Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
76267
Prove that: $x_1\cdot x_2\cdots x_n>y_1\cdot y_2\cdots y_m$.
959
Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$.
15259
Proving $\prod \limits_{k=0}^{n}(1-a_k) \geq1- \sum\limits_{k=0}^{n}a_k$
100726
Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).
49438
Prove that $X^\ast$ separable implies $X$ separable
153763
Prove that $a_1!\cdots a_k! < n!$ whenever $a_1+\cdots+a_k < n$
3786
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}\;$