Prove the non-existence of any triplet satisfying $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=1$
8383
Are there any positive integers such that $\frac{x}{y} + \frac{y}{z} + \frac{z}{x} = 1$?
25203
with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
89170
How prove this inequality $\frac{x^2y}{z}+\frac{y^2z}{x}+\frac{z^2x}{y}\ge x^2+y^2+z^2$
49209
Prove $(x+y)(y+z)(x+z)≤\frac8{27}(x+y+z)^3$
23836
Rigorous proof that $\frac{1}{3} = 0.333\ldots$
7279
$|2^x-3^y|=1$ has only three natural pairs as solutions
28274
Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer
141937
Prove that the $\lim_{(x,y) \to (0,0)}h(x,y)$ Does not Exist using Polar Coordinates
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
108801
Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$
73716
Let $x,y,z>0$ and $x+y+z=1$, then find the least value of ${{x}\over {2-x}}+{{y}\over {2-y}}+{{z}\over {2-z}}$
136782
Prove that $x * y = \frac{x+y}{1+xy}$ is a stable part of $G=(-1, 1)$
86567
Understanding $\sum_{x = 0}^y x = \frac{y(y + 1)}{2}$ in a step of a proof
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
91000
Prove that $\frac{1}{a+1}0$
91786
Proving and disproving $\exists b,c\in \mathbb R$ such that $f(x)=\frac a2x^2+bx+c $
13656
Prove existence of a real root.