Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodicity of power Fibonacci sequences modulus a Fibonacci number   Let ${\mathcal F}=(F_i:i\ge 0)$ be the sequence of Fibonacci numbers, and $j$
and $e$ be non negative integers. We study the periodicity of the power
Fibonacci sequences ${\mathcal F}^e(F_j)=(F_i^e\pmod{F_j}: i\ge 0)$. It is
shown that for every $j,e\ge 1$ the sequence ${\mathcal F}^e(F_j)$ is periodic
and its periodicity is computed. The result was previously known for ${\mathcal
F}(F_j)$; that is, for $e=1$. For $e\in \{1, 2\}$, the values of the normalized
residues $\rho_i\equiv F_i^e\pmod{F_j}$ with $0\le \rho_i<F_j-1$ are obtained.

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The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom