If $a+b=1$, show that $a^{4b^2} + b^{4a^2} \leq 1$
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
49548
If $(a + ib)^3 = 8$, prove that $a^2 + b^2 = 4$
104922
Inequality $\frac1a + \frac1b + \frac1c \leq \frac{a^8+b^8+c^8}{a^3b^3c^3}$
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
97057
Show $a^2+b^2+c^2=1$ $\implies$ $ \dfrac {b^2c^2}{1+a^2} +\dfrac {c^2a^2}{1+b^2}+\dfrac {a^2b^2}{1+c^2} \le \dfrac 14 $
50296
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
99692
Prove that $a^3+b^3+c^3 \geq a^2b+b^2c+c^2a$
30386
Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
23638
$a^2b^2+a^2c^2+b^2c^2\leq 3$
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
100571
Prove $(1-a)(1-b)(1-c)(1-d)\geq abcd$ if $a^2+b^2+c^2+d^2=1$
48211
When is $(a+b)^n \equiv a^n+b^n$?
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?