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Math Help - Primes from a pattern

  1. #1
    Super Member Bernhard's Avatar
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    Primes from a pattern

    I am a math hobbyist working through John Stillwell's book "Elements of Number Theory"

    On page 3 Stillwell after pointing out that n^2 +n + 41 is prime for all small values of n, poses the following problem:

    "Show, nevertheless that n^2 +n + 41 is not prime for certain values of n"

    Can anyone help me with this problem? I would certainly like to see a rigorous proof.
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    Quote Originally Posted by Bernhard View Post
    I am a math hobbyist working through John Stillwell's book "Elements of Number Theory"

    On page 3 Stillwell after pointing out that n^2 +n + 41 is prime for all small values of n, poses the following problem:

    "Show, nevertheless that n^2 +n + 41 is not prime for certain values of n"

    Can anyone help me with this problem? I would certainly like to see a rigorous proof.

    Simple: take n=41...

    Tonio
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    Quote Originally Posted by Bernhard View Post
    I am a math hobbyist working through John Stillwell's book "Elements of Number Theory"

    On page 3 Stillwell after pointing out that n^2 +n + 41 is prime for all small values of n, poses the following problem:

    "Show, nevertheless that n^2 +n + 41 is not prime for certain values of n"

    Can anyone help me with this problem? I would certainly like to see a rigorous proof.
    Can you show that the expression can produce numbers ending in 5 for certain values of n? (except for 5 itself obviously).
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    Super Member Bernhard's Avatar
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    Thanks Tonio

    Certainly was simple ... I supoose also that a demonstration like that is a rigourous proof.

    Bernhard
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    Quote Originally Posted by Bernhard View Post
    Thanks Tonio

    Certainly was simple ... I supoose also that a demonstration like that is a rigourous proof.

    Bernhard
    For proving an object exists, it is sufficient to produce such an object.

    Likewise, for proving a statement is false, it is sufficient to produce a counterexample.

    So, yes, it is rigorous.
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