I have read that a conjecture for Fibonacci entry points, by Paul Bruckman and Peter Anderson has been proven for prime p, that uses the Galois theory and the Chebotarev density theorem to compute the density of primes P, for which m | u.
Is it possible to calculate the distinct prime factors of the index u, for composite n, in any way?
Let un be the entry point of n, equal to the LCM of indices, from each entry point of the prime factors of n. For example, n=26,un=21 because the indices 3, and 7 are the entry points for the prime factors of n, which are 2 and 13.
These methods yield correct results for all known values. EDIT, this was apparently discovered in D. D. Wall's theorem.