subtracting exponents with different bases and finding all the prime factors of it Here is the question:
Find all prime factors of $3^{18}-2^{18}$
No Calculators allowed, and it is a competition problem, fastest answers are the best.
How can I approach this problem? If it was just $3^{18}$, it would just be 3 and likewise for 2. What do I do?

You are supposed to see it as a difference of squares and cubes to start.  $3^{18}-2^{18}=(3^9-2^9)(3^9+2^9)$ and you can factor each of these as a sum or difference of cubes.  That gets the numbers down to primes you may know, or you may need to do some trial division.
