Problem
NT-B1-M05-P019 A Small Hyperbola
#19
★★★☆☆ Level 3 of 5
Find all positive integer solutions of \(xy-x-y=1\).
Add \(1\) to both sides.
We get \(xy-x-y+1=2\), so \((x-1)(y-1)=2\). Hence \((x-1,y-1)=(1,2)\) or \((2,1)\). The solutions are \((2,3)\), \((3,2)\).
A short olympiad form of a very standard move.