When do Fibonacci invertible classes modulo M form a subgroup?
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In this paper, we look at the invertible classes modulo M representable as Fibonacci numbers and we ask when those classes, say, Fm, for a multiplication froup. We show that if M itself is a Fibonaci number, then M<8; if M is a Lucas number, then M< 7. We also show that if x>3, the number of M < x such that Fm is a multiplicative subggroup.
Annales Mathematicae et Informaticae 41 (2013), 254-270 (Proc. 15th International Conference on Fibonacci Numbers and Their Applications).