Quote:
Originally Posted by CRGreathouse
By induction. If there are 2^k divisors for the product P, and you multiply P by some prime not in P (call it q), the divisors of the new number Pq are the divisors of P, together with q times the divisors of P. Since there is no overlap (why?), there are 2^k + 2^k = 2^(k+1) divisors. Now just test the base case and you can add QED.
No.

I was able to use induction? I didnâ€™t think that I could use induction on an equation like this. It was simpler than I thought. Well, thank you very much! I perhaps should have posted this on the Mathematics Stack Exchange but figured it was related to mersenne primes since we have prime numbers and 2^k.