If x and y are non-negative integers satisfying xy+x-y=8, find all the solutions of (x,y)
Looks like Simon's Favorite Factoring Trick!
x(y+1)-y=8
x(y+1)-y-1=8-1
x(y+1)-(y+1)=7
(y+1)(x-1)=7
Case 1: y+1=1, x-1=7
(8, 0)
Case 2: y+1=7, x-1=1
(2, 6)