#1**+1 **

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

Guest Nov 30, 2019