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  • An Integer Equation

    From David Entwistle@qnivq.ragjvfgyr@ogvagrearg.pbz to rec.puzzles on Sun Aug 31 18:31:18 2025
    From Newsgroup: rec.puzzles

    This puzzle is taken from 'Advanced Problems in Mathematics', by Stephen Siklos.

    https://www.openbookpublishers.com/books/10.11647/obp.0181

    Find all sets of positive integers a, b and c that satisfy the equation:

    1/a + 1/b + 1/c = 1

    If you wish, you can read more mathematics-related problems here:

    https://books.openbookpublishers.com/10.11647/obp.0181.pdf
    --
    David Entwistle

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  • From Richard Harnden@richard.nospam@gmail.invalid to rec.puzzles on Sun Aug 31 20:16:54 2025
    From Newsgroup: rec.puzzles

    On 31/08/2025 18:31, David Entwistle wrote:
    This puzzle is taken from 'Advanced Problems in Mathematics', by Stephen Siklos.

    https://www.openbookpublishers.com/books/10.11647/obp.0181

    Find all sets of positive integers a, b and c that satisfy the equation:

    1/a + 1/b + 1/c = 1

    If you wish, you can read more mathematics-related problems here:

    https://books.openbookpublishers.com/10.11647/obp.0181.pdf

    Only three, I think:

    {2,4,4}, {2,3,6} and {3,3,3}

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  • From David Entwistle@qnivq.ragjvfgyr@ogvagrearg.pbz to rec.puzzles on Mon Sep 1 11:48:52 2025
    From Newsgroup: rec.puzzles

    On 31/08/2025 20:16, Richard Harnden wrote:

    Only three, I think:

    Me too.

    The original fractions clearly ring alarm bells when a, b or c = 0. But
    at school (many years ago) I remember being shown how to arrange the
    original equation, using the greatest common denominator, to give:

    ab + ac + bc = abc

    Now, no alarm bells. If we extend the scope to include 0, then the
    solutions for the two expressions aren't equivalent. I may have
    forgotten, but don't recall any warning that went with that process of
    finding the greatest common denominator and re-arranging to ensure none
    of the variables equal zero.

    I guess you're never too old to learn.
    --
    David Entwistle
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  • From Daniel@me@sc1f1dan.com to rec.puzzles on Mon Sep 1 21:02:12 2025
    From Newsgroup: rec.puzzles

    David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> writes:

    On 31/08/2025 20:16, Richard Harnden wrote:
    Only three, I think:

    Me too.

    The original fractions clearly ring alarm bells when a, b or c =
    0. But at school (many years ago) I remember being shown how to
    arrange the original equation, using the greatest common denominator,
    to give:

    ab + ac + bc = abc

    Now, no alarm bells. If we extend the scope to include 0, then the
    solutions for the two expressions aren't equivalent. I may have
    forgotten, but don't recall any warning that went with that process of finding the greatest common denominator and re-arranging to ensure
    none of the variables equal zero.

    But the scope of the question doesn't include 0, and there may be a
    reason for this.


    I guess you're never too old to learn.
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