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XK-TST 2012 Problem 4

    Each term in a sequence 1,0,1,0,1,0...1,0,1,0,1,0... starting with the seventh is the sum of the last 6 terms mod 10 .Prove that the sequence ...,0,1,0,1,0,1......,0,1,0,1,0,1... never occurs

    Dataset text AI-MO AoPS. Quoted with source.

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