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Math Help - [SOLVED] x^2 - y^2 = 1001 ; y>0 , Sigma(x)=?

  1. #1
    Member courteous's Avatar
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    Question [SOLVED] x^2 - y^2 = 1001 ; y>0 , Sigma(x)=?

    What is the sum of all positive integers x for which there exists a positive integer y with x^2 - y^2 = 1001?
    I (thought I) found all x:
     45^2-32^2 \leftarrow \text{ from } (7*11)*13
     51^2-40^2 \leftarrow \text{ from } (7*13)*11
     75^2-68^2 \leftarrow \text{ from } 7*(11*13)

    45+51+75=171, which is "wrong".
    I think not, but is there any other x for above equation?
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  2. #2
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    Quote Originally Posted by courteous View Post
    I (thought I) found all x:
     45^2-32^2 \leftarrow \text{ from } (7*11)*13
     51^2-40^2 \leftarrow \text{ from } (7*13)*11
     75^2-68^2 \leftarrow \text{ from } 7*(11*13)

    45+51+75=171, which is "wrong".
    I think not, but is there any other x for above equation?
    Hint: 7 * 11 * 13 = 1 * (7 * 11 * 13)
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  3. #3
    Member courteous's Avatar
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    Smile An awkward solution.

    Indeed. I would never on earth thought of that. Thank you.
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