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Homework Help: Prove or disprove, induction

  1. Dec 8, 2008 #1
    1. The problem statement, all variables and given/known data

    For all n is an element of N, n2 - n + 41 is prime
    N= natural numbers


    2. Relevant equations

    None.

    3. The attempt at a solution

    Let n=1
    12 - 1 + 41 = 41 is prime.

    n2 - n + 41 is not prime. so this hypothesis is not correct.
    assume n2 - n + 41 is not prime. there exist n that let n2 - n + 41 = n2 so n2 - n + 41 is not prime.
    therefore, when 41-n=0 this equation holds. therefore there exists a n=41 that n2 - n + 41 is not prime.
    Hence n2 - n + 41 not true for all n is an element of N.
     
  2. jcsd
  3. Dec 8, 2008 #2
    You have the right idea, that when n = 41, n^2 - n + 41 is not prime.

    Your proof doesn't make sense though. You can't begin by assuming the intended conclusion. It's not clear why there exists an n such that n^2 - n + 41 = n^2 and that this number is not prime. Work on articulating what you mean.
     
  4. Dec 8, 2008 #3

    HallsofIvy

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    Science Advisor

    That's not supposed to be a "proof" of anything. It's a perfectly valid way of finding a counter example to the supposed theorem. The "proof" that the theorem is false is simply asserting that if n= 41, n^2- n+ 41= 41^2 is NOT prime. How you got to n= 41 is not relevant to the proof.
     
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