1. Apr 26, 2009 #1

   Gear300

   

   Edit: I'm shifting to a more general question:
   If the prime factorization of an integer n is given by
   
   n = p₁^v₁p₂^v₂⋅⋅⋅p_k^v_k
   
   then what would be a proof for the number of positive divisors of n being
   
   d(n) = (v₁ + 1)(v₂ + 1)⋅⋅⋅(v_k + 1)

    

   Last edited: Apr 26, 2009

   Gear300, Apr 26, 2009
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3. Apr 26, 2009 #2

   tiny-tim

   

   Science Advisor

   Homework Helper

   Hi Gear300!
   
   Just write out the typical divisor …
   
   

   what does it look like? ​

    

   tiny-tim, Apr 26, 2009
4. Apr 26, 2009 #3

   qntty

   

   In each divisor p_i^k appear with 0 <= k <= v_i

    

   qntty, Apr 26, 2009

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