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Tags: algorithm, algebra, system of equations, number theory unsolved, number theory



The sequence of Fibonnaci's numbers if defined from the two first digits $f_1=f_2=1$ and the formula $f_{n+2}=f_{n+1}+f_n$, $\forall n \in N$. (a) Prove that $f_{2010} $ is divisible by $10$. (b) Is $f_{1005}$ divisible by $4$? Albanian National Mathematical Olympiad 2010---12 GRADE Question 4.