Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher-order Carmichael numbers   We define a Carmichael number of order m to be a composite integer n such
that nth-power raising defines an endomorphism of every Z/nZ-algebra that can
be generated as a Z/nZ-module by m elements. We give a simple criterion to
determine whether a number is a Carmichael number of order m, and we give a
heuristic argument (based on an argument of Erdos for the usual Carmichael
numbers) that indicates that for every m there should be infinitely many
Carmichael numbers of order m. The argument suggests a method for finding
examples of higher-order Carmichael numbers; we use the method to provide
examples of Carmichael numbers of order 2.

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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat