$B=((b_{ij}))$ where $b_{ij}=1 \, \forall i,j$ and $A=(a-b)i_n+bB$ Prove that $|A|=(a-b)^{n-1}[a+(n-1)b]$
2271
Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix
39779
If $a,b,c>0$ and $a+b+c=1$, prove that $\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ac}{b+ac}} \le \frac{3}{2}$.
73987
Prove the inequality $({1+\frac{a}b})^n$ + $(1+\frac{b}a)^n$ $\geq$ $2^{n+1}$
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
124320
$a,b,c>0 \text{ s.t. }a+b+c=1 \implies \sqrt{ab+c}+\sqrt{bc+a}+\sqrt{ca+b} \ge 1+ \sqrt{ab}+\sqrt{bc}+\sqrt{ca}$
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
35242
If $a$, $b$, $c$, $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$, and $\frac{a}{c}+\frac{b}{a}+\frac{c}{b}$ are all integers, then $|a|=|b|=|c|$
60006
Matrix equation: $A−A(A + B)^{−1}A = B−B(A + B)^{−1}B$
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
130543
If $a_n = \sum\limits_{r=0}^n \binom{n}{r} b_r$, prove $(-1)^n b_n = \sum\limits_{s=0}^n \binom{n}{s} (-1)^s a_s$
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
85977
Show that if $\sqrt{a}+\sqrt{b}\neq 0$, then $\mathbb{Q}(\sqrt{a}+\sqrt{b}) = \mathbb{Q}(\sqrt{a},\sqrt{b}), \forall a,b\in\mathbb{Q}$
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$