Problem
NT-B1-M12-P007 Set 2. Equation with a Product
#7
★★☆☆☆ Level 2 of 5
Solve \(xy+x+y=47\) in positive integers.
Add \(1\).
We get \((x+1)(y+1)=48\). Factor pairs of \(48\) greater than \(1\) give \((x,y)=(1,23),(2,15),(3,11),(5,7),(7,5),(11,3),(15,2),(23,1)\).
Checks full divisor enumeration.