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The converse and proving whether or not the converse holds

  1. Aug 17, 2008 #1
    What would be the converse of this conjecture, How can you prove whether or not the converse holds?

    thanks
     
  2. jcsd
  3. Aug 17, 2008 #2

    HallsofIvy

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    The converse of "If A then B" is "If B then A" so the converse of "If p is prime then np- n is divisible by p (for all n)" is "If np- n is divisible by p (for all n) then p is prime". I haven't looked at that in depth but I think you should try "indirect proof": if p is not prime, say p= ij for some integers i and j, can you find find an n so that np is not divisible by p?
     
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