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Math Help - A remainder problem.

  1. #1
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    Question A remainder problem.

    Okay, I quite didn't know which category of question this belongs to, I genuinely expect you to pardon my ignorance.
    So here is the question:

    What is the remainder obtained when the number (1010 )^1 + (1010 )^2 + (1010)^3 + .... so on till + (1010)^10 is divided by 7.

    Read (1010)^1 as 10 to the power of (10 to the power of 1)
    ''
    ^2 as 10 to the power of (10 to the power of 2)

    and so on.
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Re: A remainder problem.

    Hello, Megamind!

    According to your explanation, your parentheses are off . . .


    \text{What is the remainder when the number}

    . . 10^{(10^1)} + 10^{(10^2)} + 10^{(10^3)} + \hdots + 10^{(10^{10})}\,\text{ is divided by 7 ?}

    This is a much "bigger" problem:

    . . \left(10^{10} + 10^{100} + 10^{1,000} + \hdots + 10^{10,000,000,000}\right) \div 7
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