Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A number theoretic question arising in the geometry of plane curves and
  in billiard dynamics   We prove that if $\rho\neq1/2$ is a rational number between zero and one,
then there is no integer $n>1$ such that $$ n\tan(\pi\rho)=\tan(n\pi\rho). $$
This has interpretations both in the theory of bicycle curves and that of
mathematical billiards.

30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga