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Math Help - Find the Problem with this Proof

  1. #1
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    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?
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  2. #2
    Grand Panjandrum
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    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
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  3. #3
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    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.
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