If $k, x, y \in \mathbb{Z}$ and $k = \frac{x}{y} + \frac{y}{x}$, why is $k=2$?
62792
Can sum of a rational number and its reciprocal be an integer?
90218
Proving $\frac{x}{y} +\frac{y}{z} + \frac{z}{x} \ge 3$ for positive $x,y,z$
10444
If $\{x,\{x,y\}\} = \{z, \{z,t\}\}$, then must it be $x = z$ and $y = t$?
50283
Find answer of $\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}=4$
78118
Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?
142530
Let K be a field, and $I=(XY,(X-Y)Z)⊆K[X,Y,Z]$. Prove that $√I=(XY,XZ,YZ)$.
34430
Why does $(\frac{p-1}{2}!)^2 = (-1)^{\frac{p+1}{2}}$ mod $p$?
68990
Show that $\frac 1{1+x+y^{-1}}+\frac1{1+y+z^{-1}}+\frac1{1+z+x^{-1}}=1$ if $xyz=1$
135046
Can this quick way of showing that $K[X,Y]/(Y-X^2)\cong K[X]$ be turned into a valid argument?
102175
$Z=XY$, $E_Z[Z]$, $E_{X,Y}[XY]$
45319
Properties of $y$ if $\frac{d^2y}{dx^2}+xy=0$, $x \in [a,b],$ and $y(a)=y(b)=0.$
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
62508
If $x$, $y$, $z$ are in arithmetic progression, show that $\frac{\sin x + \sin y + \sin z }{\cos x + \cos y + \cos z} = \tan y. $
15268
Find all $x,y \in \mathbb N^*$ such that $\frac{1}{x} + \frac{1}{y}=5$
129394
understanding $\frac{\partial x}{\partial y}\frac{\partial y}{\partial z}\frac{\partial z}{\partial x}=-1$
18530
Given 4 integers, $a, b, c, d > 0$, does $\frac{a}{b} < \frac{c}{d}$ imply $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$?
28254
Why $\sum_{k=1}^{\infty} \frac{k}{2^k} = 2$?