Exact Finite-Level Block Counts for Fibonacci Sequences at Odd-Rank Prime Moduli
Year: 2026
Type: article
Abstract: This note establishes an exact formula for counting digit blocks in Fibonacci numbers modulo powers of an odd prime. If the prime’s Fibonacci rank r is odd and p² does not divide F_r, then every block of length L in digit positions j through j+L−1 occurs exactly 4r·p^(j−1) times in one complete period modulo p^(j+L). The base-5 case follows from Niederreiter’s result. The broader result is related to the p-adic framework of Bragman and Rowland. It concerns periodic arrays of Fibonacci residues and does not prove that the concatenation of Fibonacci numbers is normal.
Author: Eigler, Dieter
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225397173