Problem
NT-B2-M07-P006 An Almost Prime Product
#6
★★★☆☆ Level 3 of 5
Find all positive integer solutions of \(xy=4x+7y+9\).
Move the linear terms and add \(28\).
The equation is equivalent to \(xy-4x-7y=9\). Add \(28\): \((x-7)(y-4)=37\). Since \(37\) is prime, the only factor pairs are \((1,37)\) and \((37,1)\). Thus \((x,y)=(8,41)\) and \((44,5)\).
Slightly above basic level because of the negative shifts and the prime right-hand side.