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Math Help - Here's another Egyptian fraction puzzle for you CB

  1. #1
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    Here's another Egyptian fraction puzzle for you CB

    Can you prove in general that 4/n = 1/x + 1/y + 1/z, where n is a natural number greater than 1 and x,y and z are whole numbers? (this is the Erdos-Straus conjecture of 1948 - to date no one has proven it nor furnished a counterexample).

    The last puzzle for CB was too easy. I think this one should keep CB busy for awhile if he wants to try his hand at it.

    Good luck to everybody.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Nice one.
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  3. #3
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    I think n>=4...and not greater than 1.
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  4. #4
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    Quote Originally Posted by Pandevil1990 View Post
    I think n>=4...and not greater than 1.
    Actually Pandevil, it does start from 2 as both my book and a website agree. So, e.g., 4/2 = 1/1 + 1/2 + 1/2 (btw nowhere does the conjecture say that x,y,z have to be distinct from one another).
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  5. #5
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    Quote Originally Posted by wonderboy1953 View Post
    Actually Pandevil, it does start from 2 as both my book and a website agree. So, e.g., 4/2 = 1/1 + 1/2 + 1/2 (btw nowhere does the conjecture say that x,y,z have to be distinct from one another).
    How does posting a conjecture open for more than 60 years qualify as a puzzle (the assumption for a puzzle is that it has a solution known to the poster)

    CB
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  6. #6
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    Quote Originally Posted by CaptainBlack View Post
    How does posting a conjecture open for more than 60 years qualify as a puzzle (the assumption for a puzzle is that it has a solution known to the poster)

    CB
    You and Webster's think differently:

    "1 : to offer or represent to (as a person) a problem difficult to solve or a situation difficult to resolve : challenge mentally; also : to exert (as oneself) over such a problem or situation <they puzzled their wits to find a solution>
    2 archaic : complicate, entangle
    3 : to solve with difficulty or ingenuity <puzzle out an answer to a riddle>"

    I couldn't post this one under the math challenge section as it explicitly requires the poster to know the solution beforehand. The foreword to this section
    (If you have a brain teaser, a word problem or an interesting math problem that doesn't require formal math training, put it in here!) doesn't say anything about the poster having to need to know what the solution is to the problem.

    A puzzle doesn't require a poster to know the solution beforehand (the best kind of puzzle since it would be the most challenging). Such puzzles can be very stimulating (e.g. Fermat's conjecture which is now Fermat's last theorem or the Konisberg bridges problem which led to the new branch of topology by Euler).

    The conjecture I posted should prove to be very stimulating (I don't think it's a Godel type of problem that's impossible to solve). I'll be working at it myself and I hope others will find it stimulating.
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