How prove this $|A||M|=A_{11}A_{nn}-A_{1n}A_{n1}$
69641
Determinant identity: $\det M \det N = \det M_{ii} \det M_{jj} - \det M_{ij}\det M_{ji}$
50266
In the following figure prove that: $AK||BC$
12210
Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
120954
Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$
149700
Prove that $\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \cdots \frac{a_n^2}{a_n+a_1} \geq \frac12$
82775
if $a>1$, Prove that $\lim a^{1\over n}=1$
14581
How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
34954
If $11..11$($n$ times 1) is prime, prove that $n$ is also prime
151520
About the parity of the product $(a_1-1)(a_2-2)\cdots(a_n-n)$
80009
Prove that $| |a|-|b| | \le |a-b|$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
78144
How to prove the inequality $a_1^{a_1}a_2^{a_2}\cdots a_n^{a_n} > \left(\frac{a_1+\dots+a_n}{n}\right)^{a_1+\dots+a_n}$?
108298
Prove $\sum_{i=1}^{i=n}\frac{a_i}{S-a_i}\geqslant \frac{n}{n-1}$ and $\sum_{i=1}^{i=n}\frac{S-a_i}{a_i}\geqslant n(n-1)$.
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$