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Thread: Does anyone recognize this?

  1. #1 Does anyone recognize this? 
    Forum Radioactive Isotope MagiMaster's Avatar
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    While thinking about Goldbach's conjecture, I came across this, but I don't know if it's something either trivial or already proven or disproven.

    Anyway, the idea is this: for any odd prime, p, it's possible to find three other primes, i, j, k, distinct from p and from each other, such that .

    For example:
    2*2*5 - 11 = 3*3
    2*2*7 - 3 = 5*5
    2*2*13 - 3 = 7*7

    I've verified it by computer up to 10,000, but I don't know what to do beyond that. (The program's running to 100,000 at the moment.)

    On a side note, I think it may still work if you say i, j and k have to be odd primes, but I haven't tried that.

    Edit: My program finished, verifying it up to 100,000.
    2*7103*99133 - 17909 = 99991*99991


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  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
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    For any odd prime p, it's possible to find three other distinct primes, i, j and k, such that 2*i*j - k = p*p.

    No one recognizes that? How would you go about proving something like that?


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