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Math Help - (x+1)! + (y+1)! = x^2 x y^2

  1. #1
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    (x+1)! + (y+1)! = x^2 x y^2

    Hello, any assistance on the problem would be much appreciated. I have a vague idea but cant quite remember what to do.

    (x+1)! + (y+1)! = x^2 x y^2, how many pairs such that x and y are a pair of positive, non-negative integers?

    Any help would be great, my maths tutor set this and i honestly cant quite remember what to do in this case.
    Cheers
    Last edited by mr fantastic; July 1st 2011 at 10:23 PM. Reason: Re-titled.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: (x+1)! + (y+1)! = x^2 x y^2

    Quote Originally Posted by pikachu26134 View Post
    Hello, any assistance on the problem would be much appreciated. I have a vague idea but cant quite remember what to do.

    (x+1)! + (y+1)! = x^2 x y^2, how many pairs such that x and y are a pair of positive, non-negative integers?

    Any help would be great, my maths tutor set this and i honestly cant quite remember what to do in this case.
    Cheers
    (x+1)! > x^4 when x>4
    (y+1)! > y^4 when y>4



    (x+1)! + (y+1)! > x^4 + y^4 \geq 2x^2y^2
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  3. #3
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    Re: (x+1)! + (y+1)! = x^2 x y^2

    So is there no definite answer?? Lyk an integer answer?
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  4. #4
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    Re: (x+1)! + (y+1)! = x^2 x y^2

    Quote Originally Posted by pikachu26134 View Post
    So is there no definite answer?? Lyk an integer answer?
    ASZ has ruled out almost all the cases for you. The only remaining cases are when x \leq 4, y\leq 4. Substitute the remaining values and try to find the answer.
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  5. #5
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    Re: (x+1)! + (y+1)! = x^2 x y^2

    Does this look about right??
    M=4, N=3
    and M=3, N=4
    As in 2 pairs such that that equation is true.
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  6. #6
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: (x+1)! + (y+1)! = x^2 x y^2

    Quote Originally Posted by pikachu26134 View Post
    Does this look about right??
    M=4, N=3
    and M=3, N=4
    As in 2 pairs such that that equation is true.

    Yes! But instead of using M and N use x and y, or you can write it like that: (3,4) and (4,3) (due to the symmetric equation) .
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