Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
63958
how to prove this inequality $(ab+bc+ac)^2 ≥ 3abc(a+b+c)$
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
158844
If $a$ and $b$ are positive real numbers such that $a+b=1$, prove that $(a+1/a)^2+(b+1/b)^2\ge 25/2$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
34323
Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
30386
Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
38448
Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
125868
Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$
5927
How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$
49217
How do I show that $a^p + b^p > (a + b)^p$ for $a,b>0$ and $0<p<1$?
257
Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
118212
Is it true that $A^A\simeq P(A)$?