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Homework Help: Discrete math induction proof

  1. Mar 26, 2007 #1
    Could someone help me with this induction proof. I know its true.

    given any integer m is greater than or equal to 2, is it possible to find a sequence of m-1 consecutive positive integers none of which is prime? explain

    any help is greatly appreciated thanks
     
    Last edited: Mar 26, 2007
  2. jcsd
  3. Mar 26, 2007 #2
    Is 5! prime?
     
  4. Mar 27, 2007 #3

    HallsofIvy

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    I'm sorry, Ziox, I really don't see what that has to do with the problem. Please enlighten me.
     
  5. Mar 27, 2007 #4
    How do you know this is true?
     
  6. Mar 27, 2007 #5
    My teacher only gave us true proofs so we wouldn't be able to prove it wrong by counter example.
     
  7. Mar 27, 2007 #6
    5!+i has divisors 2,3,4,5 for i=2,...,5. Paired up respectively.
     
    Last edited: Mar 27, 2007
  8. Mar 28, 2007 #7

    HallsofIvy

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    Oh, of course! That answers the whole question. I was focusing on the "5" and didn't think about doing the same thing for n in general. Very nice.

    kai89, do you understand what ZioX is saying?
     
  9. Mar 28, 2007 #8
    You're right though, I was being pretty vague and probably would've only made sense if someone has seen it before. Should've said something about divisibility when adding.
     
  10. Mar 28, 2007 #9

    HallsofIvy

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    kai89, since it has been a couple of days now, I will give detail on what ZioX hinted at: For any positive integer n, n! is obviously divisible by every integer up to and including n. Therefore, n!+ 2 is divisible by 2, n!+ 3 is divisible by 3, up to n!+ n is divisible by by n. You have n-1 consecutive integers that are not prime.

    As I said before, very nice!
     
  11. Mar 28, 2007 #10
    Primes are so unpredictable.

    ;-p
     
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