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Math Help - Ordered Pairs Question

  1. #1
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    Ordered Pairs Question

    Hi, I've started solving this problem, but I don't know how to finish it off.

    Find all ordered pairs of integers (x,y) such that: x^2 + 2x + 18 = y^2

    so far i have completed the square to get the following:

    y^2 - (x+1)^2 = 17

    Thanks!
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  2. #2
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    You have a difference of squares. What differences of squares can give you 17?
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  3. #3
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    would (y+x+1)(y-x-1) = 17
    work?
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  4. #4
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    Quote Originally Posted by hsidhu View Post
    would (y+x+1)(y-x-1) = 17
    work?
    Yes, you have transformed the problem into one of integer factorization, which is rather easy here since 17 is prime.

    Four candidate solutions:

    y+x+1 = 1 AND y-x-1 = 17
    y+x+1 = 17 AND y-x-1 = 1
    y+x+1 = -1 AND y-x-1 = -17
    y+x+1 = -17 AND y-x-1 = -1
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