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Math Help - Great problem!

  1. #1
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    Great problem!

    Prove that the equation x^2 - y^10 + z^5=6 has no integer* solutions. Try to find a solution!
    *integer(negative, positive)
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  2. #2
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    Re: Great problem!

    Quote Originally Posted by tvavlad View Post
    Prove that the equation x^2 - y^10 + z^5=6 has no integer* solutions. Try to find a solution!
    *integer(negative, positive)
    Let's reduce this to a problem we know how to solve, shall we?

    x^2+z^5-6 = (y^5)^2 looks suspiciously like the relation from Fermat's Last Theorem. Let's start there.

    What would be your next step?

    Or, is this just a fun puzzle to challenge people on this forum for ourselves and you don't actually need help?
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