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Math Help - find all integer solotions or none

  1. #1
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    find all integer solotions or none

    For the Diophantine equation (x^4)+(5*y^3)=2008, either find all integer solutions, or show there are no integer solutions.
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    Quote Originally Posted by mandy123 View Post
    For the Diophantine equation (x^4)+(5*y^3)=2008, either find all integer solutions, or show there are no integer solutions.
    This means x^4 - 2008 = 5(-y)^3. Thus, x^4\equiv 2008 (\bmod 5) and so x^4 \equiv 3(\bmod 5) which is impossible.
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