If $a,b,c$ are positive, then $(a+b+c)(1/a+1/b+1/c)\ge 9$
15599
Given that a,b,c are distinct positive real numbers, prove that (a + b +c)( 1/a + 1/b + 1/c)>9
72882
If $a$, $b$, and $c$ are sides of a triangle, then $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$.
23694
Given that $abc=1$, prove that $\frac{b}{c} + \frac{c}{a}+ \frac{a}{b} \ge \frac{1}{a} + \frac{1}{b} +\frac{1}{c}$.
15168
If $a,b$ are positive integers such that $\gcd(a,b)=1$, then show that $\gcd(a+b, a-b)=1$ or $2$. and $\gcd(a^2+b^2, a^2-b^2)=1$ or $2 $
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
89031
Solve $a!b!=a!+b!+c!$ where $a$, $b$ and $c$ are nonnegative integers.
52305
Is there a general relation between $a/b$ and $(a+c)/(b+c)$ where $a,b,c > 0 $?
112565
Prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq \frac{9}{a+b+c} : (a, b, c) > 0$
47072
Proving the inequality $\frac{9}4\ + \frac{3abc}4\ \ge ab+bc+ca$
96327
Show that $a^x+b^x+c^x>(a+b+c)^x$ for all $a,b,c>0$ and $0<x<1$
95852
Prove that $(a+b)(b+c)(c+a) \ge8$
63931
When $ab/(a+b)$ is an integer, where $a,b$ are positive integers.
122156
An inequality concerning three positive numbers
11868
Let $a,b,c\in \Bbb R^+$ such that $(1+a+b+c)(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=16$. Find $(a+b+c)$
96027
Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite.
112676
Inequality $(a+b+c)(ab+bc+ca)(a^3+b^3+c^3)\le (a^2+b^2+c^2)^3$
76568
$a,b,c$ are real numbers $>0$. If $a+b+c=1$, show that $(a+\frac{1}{a})^2+(b+\frac{1}{b})^2+(c+\frac{1}{c})^2\ge\frac{100}{3}$