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Proof of cycle in Enigmatic Device NEERC 2009
Hi. I already solved this problem by noticing that the sequence x1, x2, x4, x8, ..., x2n modulo 2010 is periodic with period 10 and pre-period 2. This means that 
.
I would like to know a proof for this. Could you help me? You can find the problem statement here. It's the problem E.
Thanks beforehand.
