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
2*2=2+2
Hence:
\(a=\frac{b}{b-1}\)
\(b=\frac{a}{a-1}\)
Notice a and b can't equal to 1
In other words,
a+b= \(-\frac{b-2ab+a}{(a-1)(b-1)}\)
a-1 can't equal to 1
b-1 can't equal to 1
Leads to the same.
a=ab-b = b(a-1)
a=b(a-1)
a/b=(a-1)
ab=a+b
ab-a=b
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
