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Math Help - Question from the ICAS Maths competition

  1. #1
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    Question from the ICAS Maths competition

    y^3=129-x^2
    x and y must be intergers
    how many possible solutions are there?

    i have got y=5 x=+/-2 and y=2 x=+/-11

    which are 4 different possibilities now

    the question is: is it any other possibilities if y is a negative interger?
    if not, how do you prove it?
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  2. #2
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    Quote Originally Posted by chessweicong View Post
    y^3=129-x^2
    x and y must be intergers
    how many possible solutions are there?

    i have got y=5 x=+/-2 and y=2 x=+/-11

    which are 4 different possibilities now

    the question is: is it any other possibilities if y is a negative interger?
    if not, how do you prove it?
    Using thoughtless brute force methods, y=-16, x=+/-65. Can't contribute to the proof aspect (that there do/do not exist more solutions) at this time.
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  3. #3
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    Seeing it's from a math competition, there should be a better way. Try using modular arithmetic. For example you should check for solutions modulo 3.
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