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Thread: Numbery theory problem

  1. #1 Numbery theory problem 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    Ok, i have a question related to number theory.

    Prove that for each positive integer k there exist infinitely many even positive integers which can be written in more than k ways as the sum of two odd primes.

    how would i start the proof?? any help will be great
    thank you


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  3. #2  
    Forum Freshman boson31415's Avatar
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    Is it just me or is that the Goldblach conjecture or some variation of it, sorry if its not, but i'm pretty sure it is in which case no one here (or likely anywhere in the world) will have an answer.


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  4. #3  
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    that most certainly is similar to Goldbach's Conjecture.

    Quote Originally Posted by Heinsbergrelatz
    Ok, i have a question related to number theory.

    Prove that for each positive integer k there exist infinitely many even positive integers which can be written in more than k ways as the sum of two odd primes.

    how would i start the proof?? any help will be great
    thank you
    Only, it's not quite right.

    k=4.

    6=3+3. that's the only way to write the sum of 6 as 2 prime numbers and 1<4, so, as it's stated in the OP, that can't be true.
    Wise men speak because they have something to say; Fools, because they have to say something.
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  5. #4  
    Forum Radioactive Isotope MagiMaster's Avatar
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    I think you might have read that wrong. I don't think that's a working counterexample (that's only one that can't, but you'd have to show that all but finitely many can't). On the other hand, I doubt there's a proof since it seems very similar to Goldbach's conjecture.
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  6. #5  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    Thanks for the replies, alright i have an idea, what if we say umm.. a_k= the number of ways in which 2k can be written as the sum of two odd primes. Assuming where C is just some positive constant.

    so we have a mathematical statement written below;


    which from here easily leads to



    then prove that the left series is divergent and we have a proof right???
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  7. #6  
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    Quote Originally Posted by MagiMaster
    I think you might have read that wrong. I don't think that's a working counterexample (that's only one that can't, but you'd have to show that all but finitely many can't). On the other hand, I doubt there's a proof since it seems very similar to Goldbach's conjecture.
    If this is proven true, then Goldbach's conjecture is proven true. That much is obvious. I suppose the rest is interpretation of the writing, which I very well may be interpreting wrong.
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