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Math Help - prove that then n is divisible by 11

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    prove that then n is divisible by 11

    Prove that is n is a positive integer such that the alternately adding and subtracting its digits in decimal representation yeilds divisible by 11 number, then n is divisible by 11.
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    Quote Originally Posted by mandy123 View Post
    Prove that is n is a positive integer such that the alternately adding and subtracting its digits in decimal representation yeilds divisible by 11 number, then n is divisible by 11.
    n=a_0+a_1~10+a_2~10^2+...+a_k~10^k

    Now 10^r \equiv (-1)^r \mod 11

    so:

    n \equiv a_0 - a_1 + a_2 +\ ...\ +(-1)^ka_k \mod 11

    That is n is congurent to the number obtained by alternately adding and subtracting its digits in decimal representation, but n is congruent to 0 modulo 11, and therefore so is alternately adding and subtracting its digits in decimal representation.

    RonL
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