Is it true that $(a+b)^x>a^x+b^x$ for three numbers $a,b,x>1$
115176
Can we say that $\left(a+b\right)^{\alpha}>a^{\alpha}+b^{\alpha}$ for all $a,b>0$ and $\alpha>1$?
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
41792
If $abc=1$, then $\frac{a^{n+2}}{a^n+(n-1)b^n}+\frac{b^{n+2}}{b^n+(n-1)c^n}+\frac{c^{n+2}}{c^n+(n-1)a^n} \geq \frac{3}{n} $
92975
Does $a^n \mid b^n$ imply $a\mid b$?
106562
Is $3 \ge 1$ or is it just $3 > 1$?
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
12096
If $a+1/a$ is an integer, then so is $a^t+1/a^t$ for $t\in\mathbb N$
131108
Can $3p^4-3p^2+1$ be square number?
61860
Show that if $a$ has order $3\bmod p$ then $a+1$ has order $6\bmod p$.
122156
An inequality concerning three positive numbers
134348
When is $(p - 1)! + 1$ a power of $p$?
71012
If $a, b$ are positive integers such that $a|b^2, b^2|a^3,....$ then $a=b$.
141525
Cyclic Inequality $\frac{a^3}{(a+b)(a+c)}$
25258
Prove that if $ a,b,c > 0 $, then $ [(1 + a) (1 + b) (1 + c)]^{7} > 7^{7} (a^{4} b^{4} c^{4}) $.
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
137967
Are there $a,b \in \mathbb{N}$ that ${(\sum_{k=1}^n k)}^a = \sum_{k=1}^n k^b $ beside $2,3$