Find all rational solutions of $\frac{x}{x^2+4} + \frac{y}{y^2+4} = \frac{z}{z^2+4}$ or show non exist.
44250
rational number solutions to $\frac{a}{a^2+1} + \frac{b}{b^2+1} = \frac{c}{c^2+1}$ with $abc\ne 0$
8383
Are there any positive integers such that $\frac{x}{y} + \frac{y}{z} + \frac{z}{x} = 1$?
22112
Find all integer solutions to $x^2+4=y^3$.
63750
let $f(\frac{x}{3})+f(\frac{2}{x})=\frac{4}{x^2}+\frac{x^2}{9}-2$ then find $f(x)$
143194
How would you solve the diophantine $x^4+y^4=2z^2$
41890
How to get all solutions of $x^2 \equiv$ $a$ mod $p$?
18903
Finding solutions to equation of the form $1+x+x^{2} + \cdots + x^{m} = y^{n}$
41689
Find all solutions: $x^2 + 2y^2 = z^2$
13612
Show the existence of a complex differentiable function defined outside $|z|=4$ with derivative $\frac{z}{(z-1)(z-2)(z-3)}$
76679
Prove there are no other solutions of functional equation $f(x+y) = \frac{f(x)+f(y)}{1-f(x)f(y)}$
72023
Integer solutions of the equation $x^2+y^2+z^2 = 2xyz$
115244
Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
16400
Find all solutions to the equation $(z+1)^6=z^6$. Express the solutions in simplified rectangular form. Hint: Clearly $z=0$ is not a solution.
29739
How can $\frac{x^3-4x^2+4x}{x^2-4}$ be both $0$ and "undefined" when $x = 2$?
158933
Rational solutions of $y^2 = x^3 - x$
54370
If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$
150925
Finding all integral solutions of $x^4+y^4+z^4-w^4=1995$