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Math Help - Prove that x is divisible by 11 if alternate sum is divisible by 11

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    Prove that x is divisible by 11 if alternate sum is divisible by 11

    Question: Let x= (dkdk-1...d1d0)10

    Prove that x is divisible by 11 if and only if the following alternating sum is divisible by 11.

    d0-d1+d2-d3+...+(-1)kdk


    Any help is appreciated!
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    Re: Prove that x is divisible by 11 if alternate sum is divisible by 11

    Quote Originally Posted by oregongirl View Post
    Question: Let x= (dkdk-1...d1d0)10

    Prove that x is divisible by 11 if and only if the following alternating sum is divisible by 11.

    d0-d1+d2-d3+...+(-1)kdk

    Any help is appreciated!
    expand your decimal form as a sum of powers of 10.

    replace 10 by (11 - 1) and expand out using the binomial expansion. Apply mod 11

    see where that takes you
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