Well, the question didn't say a and b are two distinct numbers right?
So a possibility would be a=b
(2,2) works ,(0,0) works
Notice a and b can't equal to 1
In other words,
a-1 can't equal to 1
b-1 can't equal to 1
Leads to the same.
a=ab-b = b(a-1)
Notice a and b can equal to 0 and it works as well.
No other integer solutions other than these.
https://www.wolframalpha.com/input/?i=ab%3Da%2Bb Graph is a hyberbolic