New posts in diophantine-equations

Solving a homogeneous quadratic equation in three variables over the integers.

Natural number solutions to $\frac{xy}{x+y}=n$ (equivalent to $\frac 1x+\frac 1y=\frac 1n$)

Erdős-Straus conjecture

How to solve these two simultaneous "divisibilities" : $n+1\mid m^2+1$ and $m+1\mid n^2+1$

Curves triangular numbers.

Integer solutions of $xy+9(x+y)=2006$ [Completing a product / rectangle]

Diophantine equation $a^2+b^2=c^2+d^2$

Solutions to $ax^2 + by^2 = cz^2$

Pythagorean triples that "survive" Euler's totient function

How to find solutions of linear Diophantine ax + by = c?

$x^y = y^x$ for integers $x$ and $y$

Linear diophantine equation $100x - 23y = -19$

Find five positive integers whose reciprocals sum to $1$