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Help to solve this please ? integer problem

  1. Mar 17, 2008 #1
    we must obtain 'N' and a(i) i=1,2,3,.............,N on condition that

    the product [tex] a(1)a(2)a(3)..........a(N) [/tex] is the highest possible

    [tex] a(1)+a(2)+a(3)+........+a(N)=73 [/tex]

    every a(i) is positive

    here N (this is the hardest part) is not known and must be calculated
  2. jcsd
  3. Mar 17, 2008 #2


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    Well, since [itex]3^{1/3}>2^{1/2}=4^{1/4}[/itex], I'd suggest using as many 3s as will fit, making the rest a 2 or 4. In this case twenty three 3s and one 4 would seem to be the best. Now just check my work and make sure I didn't miss something silly.
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