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let n be an integer with decimal representation a-ka-k-1....a-1a-0
prove that n is divisible by 11 if and only if a_0-a-1+a_2.......(-1)^ka_k is divisible by 11
prove that n is divisible by 11 if and only if a_0-a-1+a_2.......(-1)^ka_k is divisible by 11