$\frac{\mathbb{C}[x,y,z]}{x^5+y^3+z^2}$ is UFD
46211
$(K[x,y,z]/(x^2+y^3+z^7))_{(x,y,z)}$ is a UFD.
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
149634
$ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
25967
Prove $\csc(x)=\sum_{k=-\infty}^{\infty}\frac{(-1)^k}{x+k\pi}$
137963
Limit of $\frac{xy-z^2}{x^2+y^2+z^2}$ and $\frac{xy}{x^2+y^2}$ as $(x,y) \to (0,0)$
12488
Show that $\frac{uu_x + vv_x}{u^2 + v^2}$ is harmonic.
123024
A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
152109
In a UFD if $x$ is irreducible, then $(x)$ is prime
117922
Is $\frac{a+b}{c+d}0$?
83557
$\frac{x^2}{y+z}+\frac{y^2}{x+z}+\frac{z^2}{x+y} \ge \frac{1}{2}(x+y+z)$
81921
If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
24864
$ \Big(\dfrac{x^7+y^7+z^7}{7}\Big)^2=\Big(\dfrac{x^5+y^5+z^5}{5}\Big)^2\cdot\Big(\dfrac{x^4+y^4+z^4}{2}\Big) $
136855
Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID
21121
Express $w$ and $1/w$ for $w=\frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3}$ in the simplest form with a rational denominator
82636
Maybe is right $\frac{n^2 + 1}{4k + 3} \notin \mathbb{Z}, n, k \in \mathbb{N}^{+}$
24413
Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD?
76694
Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$