Problem
NT-B1-M11-P015 Hidden Product
#15
★★★☆☆ Level 3 of 5
Solve \(xy=3x+2y\) in positive integers.
Move everything left and add \(6\).
We get \(xy-3x-2y=0\). Add \(6\): \((x-2)(y-3)=6\). Positive factor pairs of \(6\) are \((1,6),(2,3),(3,2),(6,1)\). Thus \((x,y)=(3,9),(4,6),(5,5),(8,4)\).
Factorisation with unequal shifts.