On number of solutions of $\frac1x+\frac1y=\frac1n$
10753
Natural number solutions to $\frac{xy}{x+y}=n$ (equivalent to $\frac 1x+\frac 1y=\frac 1n$)
44250
rational number solutions to $\frac{a}{a^2+1} + \frac{b}{b^2+1} = \frac{c}{c^2+1}$ with $abc\ne 0$
68990
Show that $\frac 1{1+x+y^{-1}}+\frac1{1+y+z^{-1}}+\frac1{1+z+x^{-1}}=1$ if $xyz=1$
151732
Number of solutions of polynomials in a field
142538
The number of solutions to an $n^{th}$ order differential equation.
124505
Proof that there must exist infinitely many solutions to a homogeneous system of equations when more unknowns than equations
144644
Solution of $\frac{dy}{dx}=\frac{1}{xy(x^2 \sin y^2+1)}$
21846
Let p be a prime. Consider the equation $\frac1x+\frac1y=\frac1p$. What are the solutions?
112512
How to prove that there are finitely many $n$ such that $f(1+1/n) = \frac{1}{n+1}$?
108885
Systems of equations with a single number
110103
Prove that there are $0<c_1 < c_2<1$ s.t. $\frac{1}{g'(c_1)}+\frac{1}{g'(c_2)}=2$ . The same for $g'(c_1)g'(c_2)=1$.
99676
Prove $\sum{\frac{1}{(x+2y)^2}} \geq\frac{1}{xy+yz+zx}$
89590
The number of solutions of $ax^2+by^2\equiv 1\pmod{p}$ is $ p-\left(\frac{-ab}{p}\right)$
69288
Number of real roots of $\sum_{k=0}^{n}\frac{x^{k}}{k!}=0$
146491
Number of solutions of $x_1+x_2+\dots+x_k=n$ with $x_i\le r$
52672
Solution of $\frac{a}{b}=\frac{a'}{b'}$ if $a,b,a',b' \in \mathbb{N}$
1001
Number of integer solutions of $x^2 + y^2 = k$