Problem
ALG-B1-M11-P018 Square of a difference
#18
★★★★☆ Level 4 of 5
Find all integer solutions of \(x^2+y^2=2xy+16\).
Move \(2xy\) to the left.
\((x-y)^2=16\), so \(x-y=\pm4\). All solutions are \((t+4,t)\) and \((t,t+4)\), where \(t\in\mathbb Z\).
Strategy: a square is hidden in the equation.