Question: Let x= (d_{k}d_{k-1}...d_{1}d_{0})_{10} Prove that x is divisible by 11 if and only if the following alternating sum is divisible by 11. d_{0}-d_{1}+d_{2}-d_{3}+...+(-1)^{k}d_{k }Any help is appreciated!
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Originally Posted by oregongirl Question: Let x= (d_{k}d_{k-1}...d_{1}d_{0})_{10} Prove that x is divisible by 11 if and only if the following alternating sum is divisible by 11. d_{0}-d_{1}+d_{2}-d_{3}+...+(-1)^{k}d_{k }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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