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March 26, 2017

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Find the solution where x and y are integers to:

1/x + 1/y = 1/14

I can use a computer to get a list of solutions:

7, -14
10, -35
12, -84
13, -182
15, -210
16, 112
18, 63
21, 42
28, 28

but I'm having trouble solving this analytically and coming to a general formula.

  • math - ,

    1/x + 1/y = 1/14

    (x+y)/xy=1/14 Inverse

    xy/(x+y)=14

    xy=14x+14y



    xy-14x=14y

    x(y-14)=14y



    xy=14x+14y

    xy-14y=14x

    y(x-14)=14x Divide with (x-14)

    y=14x/(x-14)

    Solutions:

    x-14#0
    and
    y=14x/(x-14) x#0

  • math - ,

    Do not forget that, since x and y are symmetric, they are interchangeable on your list.

    Example: if (13, -182) works, then (-182, 13) works as well.

  • math - ,

    Go to:
    wolframalpha com

    When page be open in rectangle type:
    1/x + 1/y = 1/14
    and click option =

    When you see results couple times click option: More Solutions

  • math - ,

    bosnian, i already used wolfram alpha to get the solutions I listed. I want to derive the solution analytically.

    anon, I believe you just did algebraic rearrangement.

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