Find all triples $(a,b,c)$ of positive integers such that $(1+\frac{1}{a})(1+\frac{1}{b})(1+\frac{1}{c})=3$
29971
Let $a,b,c$ positive integers such that $\left(1+\frac{1}{a}\right)\left(1+\frac{1}{b}\right)\left(1+\frac{1}{c}\right) = 3$. Find those triples.
15599
Given that a,b,c are distinct positive real numbers, prove that (a + b +c)( 1/a + 1/b + 1/c)>9
122156
An inequality concerning three positive numbers
48597
Find all ordered pairs $(a,b)$ such that $1/a + 1/b = 3/2018$ and $a,b$ are positive integers
16176
Primitive Pythagorean triple divisible by 3
18119
Show that if a,b,c,d are positive then $\frac{ab}{a+b}+\frac{cd}{c+d}\le \frac{(a+c)(b+d)}{a+b+c+d}$
142900
Find all positive integers a,b,c to the equation a!b!= a!+b!+c!
56624
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers
138216
$a,b,c$ are positive real numbers such that, $a+b+c\ge abc$. Prove that $a^2+b^2+c^2\ge \sqrt{3}abc$
101708
Integers can be expressed as $a^3+b^3+c^3-3abc$
64052
Among any three consecutive positive integers one is a multiple of 3
125210
proof: primitive pythagorean triple, a or b has to be divisible by 3
134352
The number of possible factorizations of a positive integer.
57050
$\frac{a^{3}+1}{b+1}+\frac{b^{3}+1}{a+1}$ an integer $\Rightarrow \frac{a^{3}+1}{b+1}$ and $\frac{b^{3}+1}{a+1}$ are integers.
153053
Find numbers $a, b, c$ given that $a+b+c=12$, $a^2+b^2+c^2=50$, and $a^3+b^3+c^3=168$
86413
Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1
56101
Prove the inequality $\frac{a}{c+a-b}+\frac{b}{a+b-c}+\frac{c}{b+c-a}\ge{3}$