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Math Help - Find all positive integers for an equation

  1. #1
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    Find all positive integers for an equation

    Find all possible integers n for which the equation X^3 + Y^3 = n!+4 has solutions in integers.

    I suppose the following:

    X+Y = (n!+4)^(1/3)

    Can you help finish this problem? Thanks in advance
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  2. #2
    Senior Member Sambit's Avatar
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    Quote Originally Posted by fernipascual View Post
    Find all possible integers n for which the equation X^3 + Y^3 = n!+4 has solutions in integers.
    Quote Originally Posted by fernipascual View Post
    I suppose the following:
    X+Y = (n!+4)^(1/3)
    These two are not at all same.

    All you can do is to get the values of Y from the equation: Y = ( n!+4 - X^3)^{1/3} by taking different values of X.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by fernipascual View Post
    Find all possible integers n for which the equation X^3 + Y^3 = n!+4 has solutions in integers.

    I suppose the following:

    X+Y = (n!+4)^(1/3)

    Can you help finish this problem? Thanks in advance
    As an addendum to Sambit's response, please note that \sqrt[3]{X^3 + Y^3} is not X + Y any more than \sqrt{X^2 + Y^2} is equal to X + Y.

    -Dan
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