Let n>3 be a positive integer. Find all integers k such that 1≤k≤n and for
which the following property holds:
If x1,...,xn are n real numbers such that xi+xi+1+...+xi+k−1=0 for all integers i>1 (indexes are taken modulo n), then x1=...=xn=0.Proposed by Vincent Jugé and Théo Lenoir, France JuniorBalkanshortlist2021algebraSequence