So from now on lets assume
Now since are all primes, the factors of are
Observing that , we have
Assume a solution exists. Now since q is a prime, , which is not possible since we assumed p to be prime and hence p > 1. Thus no solution exists.
We have already solved this case.
Same as (2)
Since q is a natural number, (p-2)|9 and thus p-2 can be either 1,3 or 9.
So trying all cases,
Its right but we already have tackled case.
So the solutions are the following(note that w represents any arbitrary prime):