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Math Help - Hints to prove |6^(2n)-5^m| cannot equal 9.

  1. #1
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    Hints to prove |6^(2n)-5^m| cannot equal 9.

    This is the last step to a problem I've been working on, but I have not had many ideas on how to finish this last step. n and m are positive integers. I was easily able to prove that the above could not equal 1, but I'm not sure what to apply now. Thanks.

    |6^(2n)-5^(m)|=9 can be reduced to 5^(m)-6^(2n)=9.
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    Re: Hints to prove |6^(2n)-5^m| cannot equal 9.

    Quote Originally Posted by eulcer View Post
    This is the last step to a problem I've been working on, but I have not had many ideas on how to finish this last step. n and m are positive integers. I was easily able to prove that the above could not equal 1, but I'm not sure what to apply now. Thanks.

    |6^(2n)-5^(m)|=9 can be reduced to 5^(m)-6^(2n)=9.
    If n>0 then 6^{2n} is a multiple of 9 but 5^m is not.
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