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no fibonacci number is the sum of 2000 others

Source: Moldova 2000 Grade 7 P7

April 23, 2021
number theoryFibonacci NumbersMoldovaSequence

Problem Statement

The Fibonacci sequence is defined by F0=F1=1F_0=F_1=1 and Fn+2=Fn+1+FnF_{n+2}=F_{n+1}+F_n for n≥0n\ge0. Prove that the sum of 20002000 consecutive terms of the Fibonacci sequence is never a term of the sequence.
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