Results 1 to 3 of 3

Math Help - Find the Problem with this Proof

  1. #1
    Member
    Joined
    Sep 2006
    Posts
    221

    Find the Problem with this Proof

    My task is to find the flaw with the following given proof:

    This "proof" attempts to prove that there do not exist any primes that are greater than 101.

    Proof:

    Let n > 101. Then it is evident if n is even, it's definitely not a prime.

    If n is odd, then (n + 1)/2 and (n - 1)/2 are integers. Let x = (n + 1)/2 and y = (n - 1)/2. Then, n = x^2 - y^2 = (x + y)*(x-y), thus odd n is not a prime.

    And thus the proof is complete proving that there do not exist any primes > 101.

    Q.E.D?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Ideasman View Post
    My task is to find the flaw with the following given proof:

    This "proof" attempts to prove that there do not exist any primes that are greater than 101.

    Proof:

    Let n > 101. Then it is evident if n is even, it's definitely not a prime.

    If n is odd, then (n + 1)/2 and (n - 1)/2 are integers. Let x = (n + 1)/2 and y = (n - 1)/2. Then, n = x^2 - y^2 = (x + y)*(x-y), thus odd n is not a prime.

    And thus the proof is complete proving that there do not exist any primes > 101.

    Q.E.D?
    For this to work would require that (x+y) and (x-y) are both integers !=1,
    but (x+y)=n and (x-y)=1, so n=(x+y)(x-y) is a factorosation, but not
    into factors different from 1 and n.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Ideasman View Post
    My task is to find the flaw with the following given proof:

    This "proof" attempts to prove that there do not exist any primes that are greater than 101.

    Proof:

    Let n > 101. Then it is evident if n is even, it's definitely not a prime.

    If n is odd, then (n + 1)/2 and (n - 1)/2 are integers. Let x = (n + 1)/2 and y = (n - 1)/2. Then, n = x^2 - y^2 = (x + y)*(x-y), thus odd n is not a prime.

    And thus the proof is complete proving that there do not exist any primes > 101.

    Q.E.D?
    The definition of a prime is that is has no non-trivial proper divisors. You need to show that (x+y) is proper and (x-y) is not trivial to complete the proof. But that last step is wrong.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. DEs Proof Problem
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: February 9th 2011, 12:32 PM
  2. Find the fallacy of the proof
    Posted in the Geometry Forum
    Replies: 3
    Last Post: February 15th 2010, 06:27 AM
  3. Replies: 0
    Last Post: October 27th 2009, 07:06 AM
  4. Replies: 0
    Last Post: March 16th 2009, 10:14 PM
  5. Replies: 6
    Last Post: December 14th 2008, 01:39 PM

Search Tags


/mathhelpforum @mathhelpforum