algebrainc proof for $\alpha\beta \leq \frac{\alpha^p}{p} + \frac{\beta^q}{q}$ for conjugate exponents p and q
85039
Purely "algebraic" proof of Young's Inequality
125096
Minimal polynomial of $\alpha=\sqrt 2e^\frac{2\pi i}{3}$
81842
How to prove by induction that $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$?
49217
How do I show that $a^p + b^p > (a + b)^p$ for $a,b>0$ and $0<p<1$?
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
46730
How to show $\mathbb{Q}(\alpha^{4})=\mathbb{Q}(\alpha)$?
24785
How prove this equation $\alpha=\aleph_{0}\alpha$
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
97119
Prove that $\prod_{i=1}^n(1+x_i)\leq \sum_{i=0}^n\frac{S^i}{i!}$, where $x_i\in\mathbb{R^+}$.
139674
Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$
131905
Proof for exponentiation in modular arithmetic
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
7105
Prove that $\prod\limits_{i=1}^n \frac{2i-1}{2i} \leq \frac{1}{\sqrt{3n+1}}$ for all $n \in \Bbb Z_+$
158863
How to prove $\sum_p p^{-2} < \frac{1}{2}$?
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
70129
Prove that in an ordered field $(1+x)^n \ge 1 + nx + \frac{n(n-1)}{2}x^2$ for $x \ge 0$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$