Problem
NT-B1-M05-P008 Almost a Product
#8
★★☆☆☆ Level 2 of 5
Find all positive integer solutions of \(xy+x+y=47\).
Add \(1\) to both sides.
We get \((x+1)(y+1)=48\). Thus \(x+1\) and \(y+1\) are divisors of \(48\), both at least \(2\). The solutions are \((1,23)\), \((2,15)\), \((3,11)\), \((5,7)\), \((7,5)\), \((11,3)\), \((15,2)\), \((23,1)\).
Standard practice with product completion.