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2018-01-02, 08:13   #5
George M

Dec 2017

5010 Posts

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 didn’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.