Problem
ALG-B1-M09-P017 Difference equals one
#17
★★★★☆ Level 4 of 5
Find all integer solutions of \(x^2+y^2=2xy+1\).
Move everything to one side and complete the square.
The equation is equivalent to \((x-y)^2=1\). Hence \(x-y=1\) or \(x-y=-1\). All solutions are \((x,y)=(t+1,t)\) and \((t,t+1)\), where \(t\in\mathbb Z\).
A simple form, but an important skill of giving the full answer.