The Fibonacci sequence modulo $p^2$ -- An investigation by computer for $p < 10^{14}$

Details The Fibonacci sequence modulo $p^2$ -- An investigation by computer for $p < 10^{14}$ The Fibonacci sequence modulo $p^2$ -- An investigation by computer for $p < 10^{14}$

2010-06-04

arxiv.org/abs/1006.0824v1

Mathematics

Number Theory

Scientific paper

We show that for primes $p < 10^{14}$ the period length $\kappa (p^2)$ of the
Fibonacci 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 $\kappa (p^n) = \kappa (p) \cdot p^{n-1}$ for
all primes less than $10^{14}$.

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