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Math Help - decimal expansion of 7^999,999

  1. #1
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    decimal expansion of 7^999,999

    I'm trying to figure out how to solve this problem. I have flipped thru my notes and I can't find an example of how to do this problem.

    Find the decimal expansion of {7}^{999999}.
    Thanks for the help.
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  2. #2
    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by drounds67 View Post
    I'm trying to figure out how to solve this problem. I have flipped thru my notes and I can't find an example of how to do this problem.

    Find the decimal expansion of {7}^{999999}.
    Thanks for the help.
    i don't know how many digits does this have. i didn't calculate. Use logarithms for that.
    But i can tell you the last 7 numbers in the decimal expansion.
    use euler's generalization of fermat's little theorem to get
    this implies why?
    the above two give .
    let
    so
    the inverse of 7 wrt 10^7 is 2857143(you can go to wolframalpha for this or can do some long time computing yourself )
    so,
    hence the last 7 digits of are

    i know that 7 is nothing compared to the number of digits in 7^{999999} but still...
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  3. #3
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    Hello, drounds67!

    What is the original wording of the problem?
    As stated, the problem is really difficult to answer.







    . . . . . . . . . . . . . .


    Hence: .

    . .







    So what exactly did they ask for?

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