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Math Help - Binary notation and mods

  1. #1
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    Binary notation and mods

    Express 98 in binary notation. And then perform a sequence of squarings and multiplications by 10 to evaluate 10^98 (mod 221).
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  2. #2
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    If you start with 10^n (mod 221), multiplying by 10 gives you 10^(n+1) (mod 221) and squaring gives you 10^(2n) (mod 221). So squarings and multiplications by 10 are doubling and adding 1 to the exponent.

    So the exponent 98 in binary is 1100010, which means that (reading left to right) 98=((1*2+1)*2*2*2*2+1)*2.

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