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Math Help - Index numbers

  1. #1
    Junior Member
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    Index numbers

    What is the easiest way to work out what the last 2 digits are in the expansion 5^2012? without a calculator!
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  2. #2
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    Re: Index numbers

    $5^3 = 125 = 25 = 5^2$ (mod $100$).

    Use this to show by induction on $n$, that for $n \geq 2$, that $5^n = 25$ (mod $100$).

    Hence the last 2 digits are 25.
    Thanks from topsquark
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