Possible Periods of Primary Fibonacci-like Sequences with Respect to a Fixed Odd Prime

where u0 = 05 U\ 13 and a and b are integers. We will call a and b the parameters of the recurrence. We will denote such a sequence as u(a3 b) . Two of the most important questions concerning these sequences are: For a given PFLS w(a, 2?), which odd primes have a maximal rank of apparition? and For which odd primes does the PFLS u(a5 b) have a maximal period modulo p? No definitive results are known for these questions. What we propose to do in this paper is to first present the best known results concerning these questions. Then we will turn the questions around and fix the odd prime and ask which PFLSs have maximal ranks of apparition and maximal periods with respect to that prime. In a previous paper [6]s the author obtained partial results by considering only those PFLS's u(a9 b) for which b 1.