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Number Theory

  1. Oct 14, 2008 #1
    1) Find the remainder of the division of 15! with 17

    2) If (n^2)+2 prime show that 3 divides n

    3)If p the smallest divisor for n show that there exist integers a and b such that an+b(p-1)=1

    4) For every n>1 show that n does not divide (2^n)-1

    Any help?
     
    Last edited: Oct 14, 2008
  2. jcsd
  3. Oct 14, 2008 #2

    Dick

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    Re: Number Theory HELP

    You really have to show some kind of effort (even if it's unsuccessful) before people can help. And break different questions up into different threads. But I'll give you a free hint for the first one. The integers mod 17 are a group under multiplication. Or just use Wilson's theorem. So what is 16! mod 17?
     
    Last edited: Oct 14, 2008
  4. Oct 16, 2008 #3
    Thanks

    16!=-1(mod17)
    16!=15!.16=-1(mod17)

    16=-1(mod17)

    15!=1mod17

    I dont know how to start the other problems. Any tips?
     
  5. Oct 16, 2008 #4

    Dick

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    TRY one. Make an attempt. Do anything.
     
    Last edited: Oct 16, 2008
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