Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Fibonacci sequence modulo $p^2$ -- An investigation by computer for
  $p < 10^{14}$   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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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org