Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diophantine equations involving Euler's totient function   In this paper, we consider the equations involving Euler's totient function
$\phi$ and Lucas type sequences. In particular, we prove that the equation
$\phi (x^m-y^m)=x^n-y^n$ has no solutions in positive integers $x, y, m, n$
except for the trivial solutions $(x, y, m , n)=(a+1, a, 1, 1)$, where $a$ is a
positive integer, and the equation $\phi ((x^m-y^m)/(x-y))=(x^n-y^n)/(x-y)$ has
no solutions in positive integers $x, y, m, n$ except for the trivial solutions
$(x, y, m , n)=(a, b, 1, 1)$, where $a, b$ are integers with $a>b\ge 1$.

36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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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: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an