Problem
ALG-B1-M11-P012 Fraction equation
#12
★★★☆☆ Level 3 of 5
Find positive integers \(x,y\) if \((x-4)(y-4)=16\).
Check positive divisors of \(16\).
\((x-4,y-4)\) equals \((1,16),(2,8),(4,4),(8,2),(16,1)\). Hence \((x,y)=(5,20),(6,12),(8,8),(12,6),(20,5)\).
Strategy: after transformation, only divisibility remains.