# The Fibonacci sequence modulo $p^2$ - An investigation by computer for $p < 10^{14}$ - Mathematics > Number Theory

The Fibonacci sequence modulo $p^2$ - An investigation by computer for $p < 10^{14}$ - Mathematics > Number Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: We show that for primes $p < 10^{14}$ the period length $\kappa p^2$ of theFibonacci sequence modulo $p^2$ is never equal to its period length modulo $p$.The investigation involves an extensive search by computer. As an application,we establish the general formula $\kappa p^n = \kappa p \cdot p^{n-1}$ forall primes less than $10^{14}$.

Author: Andreas-Stephan Elsenhans, Jörg Jahnel

Source: https://arxiv.org/