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On the divisibility of the rank of appearance of a Lucas sequence

On the divisibility of the rank of appearance of a Lucas sequence

Let [Formula: see text] be a Lucas sequence and, for every prime number [Formula: see text], let [Formula: see text] be the rank of appearance of [Formula: see text] in [Formula: see text], that is, the smallest positive integer [Formula: see text] such that [Formula: see text] divides [Formula: see …