Integers $x$ and $y$ with $x>y>0$ satisfy $x+y+xy=80$. What is $x$?
Find the number of positive integers solutions to $x^2 - y^2 = 105$.
How many ordered pairs $(m,n)$ of positive integers, with $m \ge n$, have the property that their squares differ by $96$?
Solve in integers the equation $2(x+y)=xy+7$.
Let $b$ and $c$ be two positive integers, and $a$ be a prime number. If $a^2 + b^2 = c^2$, prove $a < b$ and $b+1=c$.
Find all positive integer $n$ such that $n^2 + 2^n$ is a perfect square.
Solve this equation in positive integers $$x^3 - y^3 = xy + 61$$