Find all positive integer triples $(a, b, c)$ such that $(1+ \frac{1}{a})×(1+\frac{1}{b})×(1+\frac{1}{c})=2$?
61210
BMO2 1995 Question 1 - Solve the equation for positive integers (a,b,c)
20593
Show that if $a \neq b$ and a and b are positive then $\frac{a}{b}+\frac{b}{a}$ is never an integer
154716
Prove $\frac{1}{a^3+b^3+abc}+\frac{1}{a^3+c^3+abc}+\frac{1}{b^3+c^3+abc} \leq \frac{1}{abc}$
33810
Proving there are an infinite number of pairs of positive integers $(m,n)$ such that $\frac{m+1}{n}+\frac{n+1}{m}$ is a positive integer
106030
Find all the positive integer
30261
How can I find all integers $x≠3$ such that $x−3|x^3−3$
134857
Find $(a,b)$ if $x^2-bx+a = 0, x^2-ax+b = 0$ both have distinct positive integers roots
45090
Given any positive real numbers $a,b,c$, we have $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
134535
Inequality $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \geq a + b+ c$ when $abc = 1$
138216
$a,b,c$ are positive real numbers such that, $a+b+c\ge abc$. Prove that $a^2+b^2+c^2\ge \sqrt{3}abc$
76568
$a,b,c$ are real numbers $>0$. If $a+b+c=1$, show that $(a+\frac{1}{a})^2+(b+\frac{1}{b})^2+(c+\frac{1}{c})^2\ge\frac{100}{3}$
42545
If $ a,b,c\in \left(0,\frac{\pi}{2}\right)\;,$ Then prove that $\frac{\sin (a+b+c)}{\sin a+\sin b+\sin c}<1$
70006
$a,b,m,n$ be positive integers such that g.c.d.$(a,b)=1$ and $a^m+b^m|a^n+b^n$ , then $m|n$?
146294
Find all positive integers $a,b$ such that each of the equations $x^2-ax+b=0$ and $x^2-bx+a=0$ has distinct positive integral roots.
89728
Prove that $1<\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1}$
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
16382
Find $a$ such that $(x+a)(x+1991)+1=(x+b)(x+c)$ with $a,b,c\in\Bbb Z$