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General Fibonacci sequence with a property

Source: 2018 Latvia BW TST P3

June 4, 2022
algebraSequencealgebra unsolved

Problem Statement

Let a1,a2,...a_1,a_2,... be an infinite sequence of integers that satisfies an+2=an+1+ana_{n+2}=a_{n+1}+a_n for all n≥1n \ge 1. There exists a positive integer kk such that ak=ak+2018a_k=a_{k+2018}. Prove that there exists a term of the sequence which is equal to zero.
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