I also tried to solve this problem. First of all look that 2^p -1 and 2^q -1 are relatively prime. Going next we must see to situations . 2^p - 1 and 2^q -1 are composite numbers(the proof is over) and the second one when 2^p - 1 and 2^q - 1 are primes. Now I don't know how to proof that the third factor is different from any power of the 2^p -1 or 2^q - 1