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Math Help - Integer solutions to equation p^3=q^2

  1. #1
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    Integer solutions to equation p^3=q^2

    Hi, I am wondering if there are solutions to the equation p^2 = q^3, where p and q are integers (ignoring zero and one). If so, can someone give me a hint on how to find them. If not, can someone show me a proof that this is the case?
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  2. #2
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    Quote Originally Posted by borophyll View Post
    Hi, I am wondering if there are solutions to the equation p^2 = q^3, where p and q are integers (ignoring zero and one). If so, can someone give me a hint on how to find them. If not, can someone show me a proof that this is the case?

    8^2=4^3\,,\,27^2=9^3\,,\,125^2=25^3 ...can you see a pattern here?

    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    8^2=4^3\,,\,27^2=9^3\,,\,125^2=25^3 ...can you see a pattern here?

    Tonio
    ah of course, (n^2)^3 = (n^3)^2, for any n

    How could I be so dumb?
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