Problem
NT-B1-M05-P017 Product with a Remainder
#17
★★★☆☆ Level 3 of 5
Find all positive integer solutions of \(xy-x-2y=17\).
Add \(2\) to obtain \((x-2)(y-1)\).
We have \(xy-x-2y+2=19\), so \((x-2)(y-1)=19\). Since \(19\) is prime, the possible factor pairs are \((1,19)\) and \((19,1)\). Thus \((x,y)=(3,20)\) and \((21,2)\).
The prime number sharply reduces the cases.