Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a conjecture of Graham on the p-divisibility of central binomial
  coefficients   We show that for every $r \geq 1$, and all $r$ distinct (sufficiently large)
primes $p_1,..., p_r > p_0(r)$, there exist infinitely many integers $n$ such
that ${2n \choose n}$ is divisible by these primes to only low multiplicity.
From a theorem of Kummer, an upper bound for the number of times that a prime
$p_j$ can divide ${2n \choose n}$ is $1+\log n / \log p_j$; and our theorem
shows that we can find integers $n$ where for $j=1,...,r$, $p_j$ divides ${2n
\choose n}$ with multiplicity at most $o(\log n)$. We connect this result to a
famous conjecture by R. L. Graham on whether there are infinitely many integers
$n$ such that ${2n \choose n}$ is coprime to $105$.

33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat