Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Family of the Zeckendorf Theorem Related Identities   In this paper we present a family of identities for recursive sequences
arising from a second order recurrence relation, that gives instances of
Zeckendorf representation. We prove these results using a special case of an
universal property of the recursive sequences. In particular cases we also
establish a direct bijection. Besides, we prove further equalities that provide
a representation of the sum of $(r+1)$-st and $(r-1)$-st Fibonacci number as
the sum of powers of the golden ratio. Similarly, we show a class of natural
numbers represented as the sum of powers of the silver ratio.

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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
1
The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
3
The categories of this paper are: physics
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The categories of this paper are: funct-an