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Integer Prime Product

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  • Sebastian Martin
    Hello All: Can anyone prove that: For all n positive integer ;
    Message 1 of 1 , Mar 8, 2008
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      Hello All:

      Can anyone prove that:

      For all n positive integer ;

      Product[i^Floor[n/i]*(Prime[i]-1)^i,{i,1,n}]/Product[(Floor[n/i])^i*(Prime[Floor[n/i]]-1)^(Floor[n/i]) ,{i,1,n}]

      is an integer number.

      pi is the ith prime number.
      Floor[n/i] is the integer quotient of n/i.

      Sincerely:

      Sebastian Martín Ruiz




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