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a_n + a_{n+1} + a_{n+m }= 0 for all bounded sequences of integers a_n

Source: 2012 Grand Duchy of Lithuania, Mathematical Contest p4 (Baltic Way TST)

October 3, 2020
algebraSequence

Problem Statement

Let mm be a positive integer. Find all bounded sequences of integers a1,a2,a3,...a_1, a_2, a_3,... for which an+an+1+an+m=0a_n + a_{n+1} + a_{n+m }= 0 for all n∈Nn \in N.
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