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Math Help - question from my math theory module

  1. #1
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    proving an equation has no integer solutions

    show that 7x^2 - 35xy^7 + 5y^14 = 88 has no integer solutions.

    i cant find any examples similar in my lecture notes and am unsure which theories i should use to show this
    Last edited by linearalgebradunce; August 14th 2008 at 07:12 AM.
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  2. #2
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    Quote Originally Posted by linearalgebradunce View Post
    show that 7x^2 - 35xy^7 + 5y^14 = 88 has no integer solutions.

    i cant find any examples similar in my lecture notes and am unsure which theories i should use to show this
    Start by reducing the equation mod 5 and mod 7, to get
    2x^2\equiv3\pmod5,
    5y^{14}\equiv4\pmod7.
    Then concentrate on the second of those two congruences ... .
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