Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial Nullstellensatz modulo prime powers and the Parity
  Argument   We present new generalizations of Olson's theorem and of a consequence of
Alon's Combinatorial Nullstellensatz. These enable us to extend some of their
combinatorial applications with conditions modulo primes to conditions modulo
prime powers. We analyze computational search problems corresponding to these
kinds of combinatorial questions and we prove that the problem of finding
degree-constrained subgraphs modulo $2^d$ such as $2^d$-divisible subgraphs and
the search problem corresponding to the Combinatorial Nullstellensatz over
$\mathbb{F}_2$ belong to the complexity class Polynomial Parity Argument (PPA).

18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg