Ordem de aparição na sequência de Fibonacci: um problema sobre divisibilidade

Let (Fn)n≥0 be the Fibonacci sequence and let z(n) be the order of appearance in this sequence which is de ned as the smallest k ∈ N such that n divides Fk. In this work, we shall discuss some properties of this function. The main goal is to prove the existence of in nitely many solutions to the equation z(n) = z(n + 2) as well as to exhibit closed formulas for z(Fm ± 1). At rst, we shall describe the properties of Fibonacci and Lucas numbers.