For a given condition is it true that $a+b+c=3$.
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 $(a+b+c)$
18530
Given 4 integers, $a, b, c, d > 0$, does $\frac{a}{b} < \frac{c}{d}$ imply $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$?
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
76568
$a,b,c$ are real numbers $>0$. If $a+b+c=1$, show that $(a+\frac{1}{a})^2+(b+\frac{1}{b})^2+(c+\frac{1}{c})^2\ge\frac{100}{3}$
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
136868
Prove that $\sqrt{a^2+3b^2}+\sqrt{b^2+3c^2}+\sqrt{c^2+3a^2}\geq6$ if $(a+b+c)^2(a^2+b^2+c^2)=27$
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
99692
Prove that $a^3+b^3+c^3 \geq a^2b+b^2c+c^2a$
50296
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
52305
Is there a general relation between $a/b$ and $(a+c)/(b+c)$ where $a,b,c > 0 $?
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.
115719
Find the possible values of |A + B + C |
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
116933
Let $a,b,c$ be non-negative real numbers , then $\frac{(a+b+c)^2}{3}\ge a\sqrt{bc}+b\sqrt{ca}+c\sqrt{ab}$?
137626
If $a,b,c$ are positive integers,and $\cfrac{a}{b}+\cfrac{b}{c}+\cfrac{c}{a}$ and $\cfrac{b}{a}+\cfrac{c}{b}+\cfrac{a}{c}$ are integers then $a=b=c$
23869
Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive
11127
Let $a$, $b$, and $c$ be positive real numbers.