I need to prove that if are integers then is not possible.

My proof is this:

Since 101010 can be divided with 5 which is prime number, then one of factors also must be 5.

Lets assume that and .

Because it must be then it must be .

So, we have to solve system of equations in order to see whether are integers.

Since is not integer then b is not integer.

Is this proof valid?