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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 $10^{14}$.

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