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Math Help - prove that n mod 10 = d

  1. #1
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    prove that n mod 10 = d

    please can you help me with this problem
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  2. #2
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    (a) Note: 10 \equiv 0 \ (\text{mod } 10)

    So we have:
    \begin{aligned}n & \equiv d_0 + d_1{\color{red}10} + d_2{\color{red}10}^2 + \cdots + d_{k-1}{\color{red}10}^{k-1} + d_k{\color{red}10}^k \\ & \equiv d_0 + d_1({\color{red}0}) + d_2({\color{red}0})^2 + \cdots + d_{k-1}({\color{red}0})^{k-1} + d_k({\color{red}0})^k \quad (\text{mod } 10) \\ & \ \ \vdots\end{aligned}

    Use the same method for (b)
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  3. #3
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    thanks for your help

    so is that the end of the prove for a?
    and for part b, is it only i change 10 to 100?
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  4. #4
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    (a) I'm sure you can multiply 0 and d_k.

    (b) Yep.
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