MathDB
JBMO Shortlist 2021 A2

Source: JBMO Shortlist 2021

July 2, 2022
JuniorBalkanshortlist2021algebraSequence

Problem Statement

Let n>3n > 3 be a positive integer. Find all integers kk such that 1≤k≤n1 \le k \le n and for which the following property holds: If x1,...,xnx_1, . . . , x_n are nn real numbers such that xi+xi+1+...+xi+k−1=0x_i + x_{i + 1} + ... + x_{i + k - 1} = 0 for all integers i>1i > 1 (indexes are taken modulo nn), then x1=...=xn=0x_1 = . . . = x_n = 0.
Proposed by Vincent Jugé and Théo Lenoir, France
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