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!

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


    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


    User Avatar
    Staff Emeritus
    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Prove or disprove, induction