Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Two different scenarios when the Collatz Conjecture fails   In this article, we give two different proofs of why the Collatz Conjecture
is false.

32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs