For any values of $~x~$ and $~y~$ in $~e ^{x-y}~$ the result will be integer

Question

I am trying to to form a relation $(x,y)$ where x and y are real number but to be in relation it should satisfy a condition that $e^{x-y}$ should be an integer.

Could some expert please help me here in finding the values of $~x~$ and $~y~$ that satisfies the above condition.

Regards,

Rohith

Answer 1

If $$ e^{x-y}=N $$ and $N$ is a positive integer. then $$ x-y = \ln(N) $$

So your relation can be expressed as ... $$ y = x-\ln(N) $$