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Minimizing Fibb

Author: mathforces
Problem has been solved: 120 times

Русский язык | English Language

Suppose that $F_1=F_2=1$ и $F_{n+2}=F_{n+1}+F_n$, for all positive integer $n$. Let $g(n)$ be the least possible value of $| a_1F_1 + a_2 F_2+....+a_nF_n | $, where $a_i=\pm 1$, for all $i=1,2,...,n$. What is the value of $g(1)+g(2)+...+g(2020)$?

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