Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The divisibility of a^n-b^n by powers of n   For given integers a,b, and j at least 1 we determine the set of integers n
for which a^n-b^n is divisible by n^j. For j=1,2, this set is usually infinite;
we find explicitly the exceptional cases for which a,b the set is finite. For
j=2, we use Zsigmondy's Theorem for this. For j at least 3 and gcd(a,b)=1, the
set is probably always finite; this seems difficult to prove, however.
  We also show that determination of the set of integers n for which a^n+b^n is
divisible by n^j can be reduced to that of the above set.

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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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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: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn