1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    Science Advisor

    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

    User Avatar
    Staff Emeritus
    Science Advisor

    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

    User Avatar
    Staff Emeritus
    Science Advisor

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Discrete math induction proof
Loading...