Problem

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Tags: algebra proposed, algebra



interesting sequence n is a natural number and x1,x2,... is a sequence of numbers 1 and 1 with these properties: it is periodic and its least period number is 2n1. (it means that for every natural number j we have xj+2n1=xj and 2n1 is the least number with this property.) There exist distinct integers 0t1<t2<...<tk<n such that for every natural number j we have xj+n=xj+t1×xj+t2×...×xj+tk Prove that for every natural number s that s<2n1 we have 2n1i=1xixi+s=1 Time allowed for this question was 1 hours and 15 minutes.